A government consultation on the process for allowing gay couples to marry will take place next March.
A Downing Street source said Mr Cameron had “personally intervened” to ensure that the consultation takes place and that the law is changed within the lifetime of this parliament.
Equalities minister Lynne Featherstone announced earlier this year that a consultation would begin after Peter Tatchell and other gay rights campaigners lobbied for full equality.
The consultation will only cover civil marriage for same-sex couples – not religious marriage. Some faiths, such as the Quakers, have called for the right to hold gay marriages.
Furthermore, the consultation will not specifically address the issue of civil partnerships for opposite-sex couples, which are currently not legal.
The wording of today’s announcement says the consultation will consider “how” – rather than “if” – to open up civil marriage to all couples.
Ms Featherstone said: “I am delighted to confirm that early next year, this government will begin a formal consultation on equal civil marriage for same-sex couples.
“This would allow us to make any legislative changes before the end of this parliament.
“We will be working closely with all those who have an interest in the area to understand their views ahead of the formal consultation.”
In a separate move, the government is also planning to allow the first religious civil partnerships in the new year.
Stonewall chief executive Ben Summerskill, who has criticised the government for delaying the consultation, commented: “We welcome this announcement as warmly as we welcomed the previous two announcements that consultation on extension of the legal form of marriage was about to start.
“We look forward to the government honouring its pledge that this legislation will be passed by 2015.”
But Mr Tatchell questioned the need for any consultation at all, adding: “It is really offensive for the government to exclude from this consultation any discussion about opening up civil partnerships to heterosexual couples. The current ban on straight couples is outright discrimination, which the government apparently plans to retain.
He added: “It is an insult to people of faith for the equality minister to rule out any repeal of the ban on religious organisations conducting same-sex marriages. Some faith organisations, such as the Quakers and Unitarians, have expressly requested that they should be allowed to do so.”
Civil partnerships for gay couples were legalised in 2005 but gay rights campaigners argue that a two-tier system is discriminatory.