David Cameron has confirmed reports that he is to back same-sex marriages for religious institutions.

Speaking after an event in Redditch on Friday afternoon, the prime minister said: “I’m a massive supporter of marriage and I don’t want gay people to be excluded from a great institution.

“But let me be absolutely 100% clear, if there is any church or any synagogue or any mosque that doesn’t want to have a gay marriage it will not, absolutely must not, be forced to hold it.

“That is absolutely clear in the legislation.

“Also let me make clear, this is a free vote for Members of Parliament but personally I will be supporting it.”

Mr Cameron first raised the prospect of marriage reform when he responded to a PinkNews.co.uk question on equal marriage by saying in 2010: “I want to do everything I can to support commitment and I’m open to changing things further to guarantee equality.”

Benjamin Cohen, of Out4Marriage said: “We’re delighted to hear that the government will be legislating to introduce full equal marriage including same-sex marriages solemnised by religious ministers.

“The prime minister and deputy prime minister both told us during the summer that such a move had their personal support. We’re glad that this personal support is being translated into government action.

“Legislation must give individual religious organisations the freedom to decide for themselves whether to hold same-sex marriages. None should be forced to, but those that wish to must be given the rights to do so.”

Ruth Hunt, the director of public affairs at gay rights charity Stonewall, said: “We’ve long campaigned to allow religious organisations to conduct same-sex marriages if they wish to do so.

“This is an important issue of religious freedom and many gay people of faith will welcome proposals allowing them to celebrate their marriages with their pastors and fellow congregants.”

Meanwhile, on Friday afternoon, Scotland’s Equality Network tweeted: “Scottish Govt have been clear all along that churches that want to do equalmarriage will be able to. Good news that UK Govt now says same.”

The charity’s policy coordinator Tom French also tweeted: “Great news – UK Government set to follow in footsteps of Scotgov & introduce same-sex religious marriage too! equalmarriage.”

However, Tory MP Mark Pritchard said he feared exemptions for places of worship were likely to be ruled unlawful by the Supreme Court or the ECHR despite government assurances it would not be.

“Same-sex marriage Bill now exercises Tory grassroots as much as lack of progress on a referendum. Number 10 should hear the alarms bells,” he said on Twitter.

The MP added that the policy would “undo much of the good outreach work the [Conservative] Party has done with Muslim, Sikh, and Hindu communities”.

Stewart Jackson, the Conservative MP for Peterborough and a member of the Public Accounts Committee, tweeted: “Gay marriage bill will be massacred in the Lords and govt can’t use Parliament Act as it wasn’t in manifesto. Arrogant Cameron knows best.”