The poll, taken in the days following the London bombings, found 51% in favour of such a move but 44% against.
The proposed new law is meant to protect people of all faiths from abuse but critics say it curbs free speech.
The poll of 1,005 people found those who were religious almost as likely to be against it as those who were not.
The survey, which was commissioned as part of a BBC News website series on faith in the UK, found strong support for laws that respect and are influenced by religious values.
There was a more divided picture when it came to the broadcast of material that might cause religious offence.
It also explored attitudes to homosexuals and women holding religious office, following the recent controversy over gay clergy and the Church of England backing the ordination of women bishops.
Approval for laws respecting religious values was, not surprisingly, high among those who belonged to religions, but even among those with no religion 3% more were in favour than against.
Some 49% of all respondents said broadcasters "should not avoid language or story lines which might cause any of the main religious groups to take offence", with 45% saying they should.
Among religious people, 45% thought broadcasters should avoid causing offence, but a greater number, 49% thought they should not. Among non-religious people, 45% thought offence should be avoided, and 51% felt it should not.
There was a gender divide on this issue too, with 42% of men saying broadcasters should avoid causing religious offence, compared to 48% of women.
The Racial and Religious Hatred Bill currently going through parliament would create a new offence of incitement to religious hatred and would apply to comments made in public or in the media, as well as through written material.
The aim is to protect people from incitement to hatred against them because of their faith.
But ministers insist it will not ban people - including artists and performers - from offending, criticising or ridiculing faiths.
In the BBC's poll, 51% supported legislation "aimed at preventing abuse or inciting hatred of people because of their religious faith".
But 44% thought "stopping people from criticising those with other religious beliefs is an unjustified limit on free speech".
Among people belonging to religions, a category which included Christians, Muslims, Hindus, Sikhs, Jews and other faith groups, 43% were opposed to a ban, compared to 44% among people with "no religion".
In January an ICM poll for The Guardian newspaper suggested stronger public support for incitement to religious hatred laws.
The poll found 57% agreeing a ban was "needed to stop those who want to stir up hatred against people of particular religious faiths".
It found 36% said the new law was "wrong because people should be allowed to express their opinions freely, however hateful".
The BBC/ICM poll is based on interviews with 1,005 people between 8 and 11 July this year.
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One cannot simply legislate away problems. This Bill can only be weak or open to 'common sense' interpretation. If the former, it's a waste of time; if the latter, I offer up the old adage that 'common sense isn't always common practice'.
Stephanie Boyd, Edinburgh, Scotland
The state apparatus has no place in any religious discussion. Free speech all the way - even if I dislike what you have to say - there is a difference between expressing an opinion and acting upon it - and we already have laws that handle the latter well enough.
Andy, Glasgow, UK
What next? An offence of criticising political beliefs? This is an affront to free speech and will prevent any rational examination of all religious beliefs no matter how deserving of, or in need of such examination they might prove to be. No religion, or any other philosophy, or belief system, should be afforded such protection. It is dangerous to do so.
Phil Andrews, Essex, UK
Outlawing religious hatred, yes. Stopping an lapsed-to-ex Catholic like the late Dave Allen from poking fun at his own faith - definitely not.
Ken, London, UK
I think that the question that "laws should respect and be influenced by UK religious values" has been wrongly formulated. I, as well as most other people that are not religious, agree with many values that are shared by the main religions (like caring for other, especially weaker people). So, these values should be respected by our laws. But I am horrified by religions dictating non-humane laws that constrict freedom or equality between sexes.
Steven Kolenberg, Luxembourg
Many "holy books" contain lots of passages that are easy to construe as inciting religious hatred, and should therefore be among the first things to be banned under the proposed legislation, if it's interpreted honestly and without prejudice. Religious people should be careful not to saw off the tolerant, secular humanist branch they're sitting on.
Bill, London, UK
It is dangerous to have any Bill going through parliament backed by promises that of course it wouldn't be misused: it is only the courts that can decide how to interpret the law. I am very worried that as it stands the incitement to religious hatred Bill is much too vague and open to abuse.
Jamie, Luton, Beds
Surely any reasoned enlightened study of religion is likely to lead to its ridicule? This will most likely cause offence and the legislation will be enacted. The Government's position in therefore unsustainable. Thinkcrime is here, 21 years overdue.
If people of faith could provide some evidence that God exists, then I would be in favour of the law. Until then it's just a law protecting the superstitious.
It is good enough for us to let sleeping dogs lie. Frankly speaking, where does one draw the line? And most especially, it may be very subjective in application.
Namdi Onwuachu, Milton Keynes, UK
Your poll on hate laws is deeply flawed. The two options offered are not really alternatives to each other and certainly not mutually exclusive, yet you did not offer a 'both' option. I'm sure many people (like me) back new laws to prevent the incitement of religious hatred, but also think that criticism of religion should be permitted and is possible within the scope of such a law.
Rob, Leeds, UK
Hopefully these statistics will not influence the powers that be as you cannot count on the opinion of anyone who declares to be of no religious belief, since the proposed bill is not likely to affect them.
Tracie Yebovi, London
It is the rest of us non-believers (the majority in the UK) that need protection from the religious. Salman Rushdie is still on the run, the play that offended some Sikhs is still closed, and blasphemy is still on the statute books to protect the Church of England.
The law would need to make it very clear what constitutes an offence if this legislation goes through. The core of this country, and indeed the 'Free West', is Freedom of Speech, and let us not forget the millions who died defending it in the First and Second World Wars.
I think it would be unfortunate if people's freedom of expression was restricted by whatever a particular group deems as offensive. Overtly inciting hatred on any particular group (religious or otherwise) is obviously wrong and I think that it is right to have laws to control this. However I think the boundaries of acceptability should be clearly defined by the government and not by the standards of the most intolerant group.
Robert, Cambridge, UK
I am not in favour of any law that restricts the right to express freedom of speech and most vehemently against religious organisations dictating government policies and peoples thinking.
John Marshall, Preston, England
As a Muslim, I feel that these laws are unnecessary. Yes, I may appreciate the security it will offer my religion, but I strongly believe that as Muslims, we cannot stifle open discussion and debate - we have been around for more than 1400 years, and we are more than capable of defending our religion, as are other religions.
Ziyad Abubacker, Luton
Faith, like anything else, should be subject to criticism. There should be a clear distinction in the law between 'faith' and the practitioners of the faith. There should also be a discussion on where faith ends and culture begins. Culture can corrupt faith and faith can corrupt culture. There are just too many nuances for the law to tackle at the moment.
Suzannna, Cork, Ireland
As this law would not affect comedians, artists and other performers, it is highly probable that programmes such as 'Jerry Springer The Opera' would be free from sanction as it's 'comedy'. Whereas people like myself who preach the gospel would be hauled off to jail for 'incitment to religious hatred'. As a Christian I already feel marginalised in this country, this bill will only add to that feeling.
I can agree with a Bill "preventing abuse or inciting hatred of people because of their religious faith". However, I also agree that "stopping people from criticising those with other religious beliefs is an unjustified limit on free speech". The poll tells us nothing. There is a world of difference between incitement to hatred and legitimate criticism. For instance, I could criticise a minister or priest for giving boring sermons. But I would not thereby seek to encourage anyone to hate either that minister/priest or the religion he represents.
Rob Mackenzie, Edinburgh
I think this the section of this bill that covers religious hatred is the most sinister law the present Government have yet tried to bring in. No matter what it actually says, it is the kind of bill that opens the way for self-censorship, and so in the long run I suspect will lead to a general presumption among news media against broadcasting or publishing anything that might question religious faiths. This at a time when the need for such questioning is more relevant than it has ever been.
Peter Baber, West Yorkshire
I think the incitement to religious hatred laws will close down free speech and thoughtful debate about the truth claims of religions/secularism. We need to engage with these ideas, not disengage, which is what these laws will inadvertantly achieve.
Mark Birri, New Barnet, England
I think it is important that any proposed laws on banning incitement to hatred based on religion should be fashioned so as to still allow free speech and the exchange of ideas. It should be possible to criticize a religion or philosophy without criticising individuals who practise it. If I am born into a religion, it is unfair that people criticize me personally for my beliefs; however it is important to be able to challenge the basis/structure/legal aspects of the religion itself.
John Gibbons, Galway Ireland
The touchstone should be the fact of incitement to hatred. That needs to be curbed - by making speakers accountable for the results of their words. But it is virtually impossible to stop some people being offended. Freedom of speech is too precious to be sacrificed to the sensibilities others.
Nick Woods, Great Yarmouth UK
I do not understand why religions should be singled out as ideologies that need 'special protection'.
Ralf, Brighton UK
It is very dangerous to bring in a law which has the capacity to prevent people from criticising religion. Whatever the intention of the law, that side effect is inevitable. The introduction of this law will see more fanatics hide behind the shield of their faith, and the integration that needs to take place simply won't happen.
David Mercier, Kent, UK
I believe that Free Speech trumps a hate speech law. Then again an over the top hate statement should have some kind of remedy. They use to say that the marketplace will sort it out and, of course, if it isn't broadcast it becomes a tree falling in an empty forest. Still, I side with free speech.
John Joyce, Southampton , NY , USA
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