Mr Murphy has previously been introduced to the Pope by Cardinal Keith O'Brien
The Roman Catholic Church in Scotland has accused the Labour government of conducting a "systematic and unrelenting attack on family values".
The attack came as Scottish Secretary Jim Murphy, a practising Catholic, claimed religious faith had a role in British politics.
Mr Murphy said in a lecture that Labour best represented people of faith.
But Scotland's most senior Roman Catholic accused the government of "undermining religious freedom".
And a spokesman for the Scottish National Party said Mr Murphy was guilty of "crude electioneering" by trying to "corner the market regarding people's faith".
A tangible example by the government over the last decade that it acknowledged or endorsed religious values would also have been welcomed
Cardinal Keith O'Brien
Mr Murphy focused on the key part "values voters" can play in the election when he delivered the Progress lecture in London on Tuesday evening.
He argued that faith values have always been "at the very foundations of the Labour Party".
In his lecture, the Scottish secretary said: "In the US, faith has long played a central part in politics. Not surprising for a country where 60% of people say that God plays an important part in their lives.
"But it's wrong to think that it plays no role in British politics."
The MP for East Renfrewshire added: "Faith voters massively outweigh 'Motorway Men' or 'Worcester Woman' or any other trendy demographic group identified by marketeers."
He also told the audience that like faith, the family was "another force for good" and "the most important thing in our country".
The minister added: "As well as providing a supportive intellectual environment, it's a potential source of financial support in difficult days."
His comments were in contrast to the stated attitude of former Labour communications chief Alastair Campbell.
Despite former prime minister Tony Blair's strong religious faith, Campbell famously said: "We don't do God".
Mr Blair himself said he had avoided talking about his religious views while in office for fear of being labelled "a nutter".
Jim Murphy said religion was at the "very foundations" of the Labour party
Cardinal Keith O'Brien, the leader of the Roman Catholic church in Scotland, welcomed Mr Murphy's "recognition of the role played by faith and religion in society".
But he added: "A tangible example by the government over the last decade that it acknowledged or endorsed religious values would also have been welcomed.
"Instead we have witnessed this government undertake a systematic and unrelenting attack on family values. This is a charge I personally put to Gordon Brown when we met in 2008 and I have seen no evidence since then to suggest anything has changed."
Ironically, Mr Murphy had been due to mention the Cardinal by name in his speech by saying: "When the Cardinal speaks, people listen."
Conservative leader David Cameron recently spoke of the importance of his Christian faith, while acknowledging that it grew "hotter and colder by moments".
He said he did not have a "direct line" to God and did not pray for guidance from the almighty.
Liberal Democrat leader Nick Clegg has said he did not believe in God.
However, he later added he had "enormous respect for people who have religious faith", that his wife is Catholic and that his children are being brought up Catholic.
A spokesman for Scottish First Minister Alex Salmond said: "Politicians are fully entitled to declare their personal testament, as the first minister has done and indeed would encourage others to do so.
"However, it is quite a different matter to make any suggestion that a political party should seek to corner the market regarding people's faith.
"To do so would be absurd, unreal, and bear the hallmarks of crude electioneering, which would backfire rather badly.
"The reality is that people of all faiths and none support the different parties in Scotland, and that forms part of the vibrant political system we have."
Terry Sanderson, president of the National Secular Society, said: "Jim Murphy is taking the Labour Party into dangerous territory when he calls on it to make a special play for the religious vote.
"His personal religious enthusiasm may be blinding him to the facts. It is no longer the case that clerics can dictate the way their congregations vote. People are too independent-minded now to be herded into the voting booth by religious considerations alone."
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