London Mayor Boris Johnson and Education Secretary Michael Gove are among more than a dozen senior Conservatives who have launched a new group to campaign for gay marriage.
David Cameron supports the plans to allow same-sex weddings to be held in places of worship and has promised a free vote, but more than 100 Tory MPs are expected to oppose the change in the Commons next year.
The new group has been put together by Nick Herbert, the former police minister who resigned from the Government in September's reshuffle.
As well as Mr Johnson and Mr Gove, it includes Transport Secretary Patrick McLoughlin, who is Catholic, Foreign Office minister Alistair Burt, an evangelical Christian, former Tory ministers Lord Fowler and Nicholas Soames and Scottish Conservatives leader Ruth Davidson.
In a letter to The Sunday Telegraph announcing the formation of the group, the 19 declared: "Marriage should be open to all, regardless of sexuality.
"We recognise that civil partnerships were an important step forward in giving legal recognition to same sex couples.
"But civil partnerships are not marriages, which express a particular and universally understood commitment."
Mr Herbert, who is in a civil partnership, said changing the law was "the right thing to do".
"It is precisely because marriage is such a uniquely important institution that we should ensure that all couples who want to enter into it, regardless of their sexuality, can do so," he added.
"Conservatives who believe in marriage should feel this most strongly."
However, Mr Herbert insisted it would be wrong to "compel religious organisations to marry same-sex couples against their will" and called for legal "safeguards" to prevent it.
Under the proposals, due to be fleshed out this week, churches and other venues will be allowed to "opt in" to holding civil marriage ceremonies.
Ministers will offer a guarantee that no institution will be forced to marry gay people on their premises - but Tory MPs and religious groups have questioned whether it would stand up to challenges under the Human Rights Act.
Legislation is expected to be introduced before Easter, and could take effect about a year later - with the first ceremonies likely be held in spring 2014.