Speaking in the Commons during prime minister's questions on Wednesday, Cameron said he was "a marriage man" and to expand civil partnerships would "weaken" the institution.
Yesterday's free vote tore the Conservative Party in half, with 136 Tory MPs registering opposition, compared to just 127 - including Mr Cameron - who endorsed the proposals at second reading.
As the Commons backed the proposals by a big margin of 400 to 175, environment secretary Owen Paterson and Welsh secretary David Jones voted against, while fellow Conservative cabinet ministers Philip Hammond, the defence secretary, and attorney general Dominic Grieve stayed away.
In the wake of the vote, backbench Tory MP Christopher Chope, who voted against gay marriage, asked Cameron to look at giving heterosexual couples an equal right with homosexuals to enter civil partnerships.
Cameron rebuffed the proposal, telling Chope: "Frankly, I am a marriage man. I am a great supporter of marriage - I want to promote marriage, defend marriage, encourage marriage.
"The great thing about last night's vote is that two gay people who love each other will now be able to get married, and I think that is an important advance.
"I think we should be promoting marriage, rather than looking at any other way of weakening it."
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Labour's Diane Abbott said last night's vote was a victory for equality and demonstrated that while the "arc of history" may move slowly, it "bends towards justice".
Cameron replied: "I agree very much. I think last night's vote will be seen not just as making sure there is a proper element of equality but also helping us to build a stronger and fairer society.
"I thought many of the speeches made last night were very moving, very emotional and I would pay tribute to all those people who have actually made this case, some of them for very many years, saying they want their love to count the same way that a man and a woman's love for each other counts.
"That is what we have opened now in this country and that is why I'm proud it is this government that has brought it forward."
The Labour Party has also dodged the question of whether civil partnerships should be open to heterosexual couples.
During the Commons debate yesterday, shadow equalities minister Yvette Cooper told Chope civil partnerships were a "separate issue".
"I am sure that there will be a debate on that in due course later in our consideration of the Bill, and I know that people have different views on it. I believe that the case for equal marriage is a very powerful one," she said.Suggest a correction