Jim Murphy, the Scottish secretary, has been accused of staging a “crude political stunt” after inviting the Pope and US president Barack Obama to visit Scotland.

Opponents said the minister was guilty of electioneering by seeking to cash in on the Catholic vote and on Obama’s popularity.

The SNP says it is an attempt to try to “out-statesman” Alex Salmond, the first minister, who scored a PR coup when he secured a personal audience with Hillary Clinton, the US Secretary of State, last week.

Murphy, who was responsible for relations with the Vatican as Europe minister, has asked Gordon Brown to facilitate a visit by Pope Benedict XVI. The prime minister used an official visit to the Vatican last month to invite the 81-year-old to Britain, after presenting him with the gift of an Iona cross.

The last papal visit to this country was by Pope John Paul II, who celebrated mass with 300,000 people in Bellahouston Park, Glasgow, in 1982. While welcoming any possible visit, politicians said Labour’s real motivation was to win back voters who have defected to the SNP.

Last year the party lost the safe Glasgow East seat, which has a high number of Catholic voters, after Bishop Joseph Devine accused it of “violating moral law” and “losing ethical credibility”.

In an attempt to win back favour, Labour has signalled it will finally scrap the Act of Settlement 1701, which prevents Catholics from inheriting the crown. Party strategists also hope that Brown’s visit to the Vatican will play well to Catholic voters.

Murdo Fraser, the deputy Scottish Conservative leader, said: “Given that there has not been a lot of indications from the present Pope of his interest in travel to the extent of John Paul II, you have to wonder if it’s a realistic prospect, or is it just a pretty crude attempt by an increasingly desperate party to shore up what they see as some of their core vote?

“I can only imagine they’ll be looking at any stunts they can come up with.”

Kenneth Gibson, an SNP MSP, said: “This is a childish attempt at one-upmanship.”

Murphy met the Pope last year in his capacity as Europe minister and said at the time that it was a “wonderful opportunity which I will never forget”. He said it would be for Downing Street, Buckingham Palace and the Vatican to work out the details of a papal visit but that the feedback so far has been “positive”.

A senior Catholic church source warned: “It is no coincidence that since the loss of Glasgow East there have been a number of attempts to win favour with us but people are mindful that the government ignored the church’s opposition on embryology and sexual orientation legislation.”

The date of any UK visit is not clear, according to Murphy, although Brown has said the pontiff could visit as soon as he wants. The Vatican declined to comment.

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