The call comes from 61 faith leaders in a letter to the party leaders on the eve of major votes in the House of Lords on Tuesday.
The letter has been signed by Christians, Muslims, Jews and Buddhists. Christian signatories include the Catholic Archbishops of Southwark and Cardiff, the General Superintendant of Elim Pentecostal Churches, and the head of the Coptic Orthodox Church in the UK.
They warn legalising gay marriage will have "serious and harmful consequences for the health of society, family life, and human rights such as freedom of religion and of speech".
They express disappointment that the Government has "failed" to engage the faith community in "meaningful debate" on the issue and say that the speed with which the legislation is being pushed through Parliament means it has been subject to "wholly inadequate scrutiny".
"Marriage between a man and a woman is the fundamental building block of human society. These proposals would radically undermine the nature and place of the family in our society. We cannot believe that this is what you intend and therefore ask you to pause before taking such a damaging step," they wrote.
There is also scepticism about the effectiveness of safeguards in the long term for those with a traditional view of marriage.
"We are unconvinced by the safeguards upon which your Government have placed such emphasis. Some of Britain's most eminent scholars and lawyers emphatically say that these are legally unsustainable. Moreover they are seriously limited in their scope," the letter reads.
"They do not protect or apply to those who work in either the public or private sectors. They will not protect the teacher or the parent who, for religious, or philosophical reasons, supports the current definition of marriage.
"Already we have seen cases of those who back traditional marriage being sacked or demoted. These consequences of the proposed legislation are clearly unacceptable."
Religious leaders to have signed the letter include Archbishop Peter Smith, Bishop Michael Nazir Ali, Sir Iqbal Sacranie, Shaykh Suliman Gani, Bishop Doye Agama, Bishop Angaelos, Archbishop Bernard Longley, Rabbi Natan Levy, Archbishop George Stack and Mr Farooq Murad.
Canon Chris Sugden, one of the organisers of the letter, said the unity among faith leaders demonstrated the widespread concern about the plans.
"The Government seems determined to rush this legislation through Parliament without even the pretence of proper scrutiny. They either failed to engage with all religious leaders or deliberately ignore many. Instead they have preferred to promote the impression that those opposing this change were just a few white elderly Christians," he said.
"It is both unfair and disingenuous to try and portray the opponents of the redefinition of marriage as nothing more than extras from the Vicar of Dibley. There is widespread opposition to these plans from every major religion."
With some Christians already losing their jobs or being disciplined because of their views on homosexuality, Canon Sugden suggested there would be more incidents like this after gay marriage has become law.
He continued, "These proposals have never been voted on by the British public, never appeared in any manifesto, in a Queen's Speech, White, or Green Paper.
"Coupled to the democratic deficit, the inadequate scrutiny and safeguards will create the perfect storm for those who support traditional marriage."