The British National Party has printed one of the controversial cartoons satirising the Prophet Muhammad on its website and in a campaign leaflet.
The British National Party is led by Nick Griffin
It is placed next to a photo of a cartoons-inspired protest in London showing placards urging violence against anyone who insulted Islam.
The BNP leaflet asks people which of the two "you find offensive".
Labour said the tactics were from the "Nazi textbook". Tories said the BNP had sunk to "despicable levels".
A BNP spokesman said: "We are a democratic party which wants a debate."
A series of cartoons, some depicting the Prophet Muhammad as a terrorist, were originally published by Danish newspaper Jyllands-Posten late last September to accompany an editorial criticising self-censorship in the Danish media.
Islamic tradition prohibits any depiction of Allah or the Prophet.
Following further publication there have been violent demonstrations in several Islamic countries.
No major British newspaper has shown them.
BNP spokesman Phil Edwards told the BBC News website the aim was to encourage further discussion of the issue.
He added: "We are the only political party which wants the debate. We don't know what the answer is going to be."
Mr Edwards said it was the party's "fundamental principle" to "protect and preserve our traditional culture and identity", saying the BNP was not "in thrall to political correctness".
For the Conservatives, shadow home secretary David Davis said: "This is yet another example of the despicable levels to which the BNP will sink."
Labour Party chairman Ian McCartney said: "Their tactics are becoming increasingly sophisticated but they always involve blaming one part of the community for local problems.
"They take up legitimate local grievances and they exploit those issues for their own racist aims.
"The BNP's strategy is straight out of the Nazi textbook."
The BNP, which has 19 councillors, received 0.7% of the total UK vote in the General Election last year, and 4.9% of the vote in the 2004 European Parliament elections.
It says it will be putting up hundreds of candidates in the local authority elections in England on 4 May.