Same-sex marriage is "an important step forward" and will "make our society stronger", David Cameron has said.
The prime minister's intervention came shortly before MPs were due to vote on plans to legalise gay marriage in England and Wales.
A number of Conservative MPs have spoken out against the plans - one calling the idea "Orwellian".
But Mr Cameron said he backed marriage for all couples because it was right and it promoted commitment.
"Today is an important day. I am a strong believer in marriage. It helps people commit to each other and I think it is right that gay people should be able to get married too," he said.
"This is, yes, about equality. But it is also about making our society stronger. I know there are strong views on both side of the argument - I accept that. But I think this is an important step forward for our country."
The Marriage (Same Sex Couples) Bill would enable same-sex couples to get married in both civil and religious ceremonies, where a religious institution had formally consented, in England and Wales.
It would also allow couples who had previously entered into civil partnerships to convert their relationship into a marriage.
Minister for Women and Equalities Maria Miller told MPs: "What marriage offers us all is a lifelong partner to share our journey; a loving stable relationship to strengthen us and a mutual support throughout our lives.
"I believe this is something that should be embraced by more couples. The depth of feeling, love and commitment is no different between same-sex couples than opposite-sex couples."
Mrs Miller argued that marriage had evolved over time and rejected the claim that there was no need for same-sex marriages because same-sex couples can already have a civil partnership.
"A legal partnership is not perceived in the same way and does not have the same promises of responsibility and commitment as marriage," she said.
"All couples who enter a lifelong commitment together should be able to call it marriage."
She acknowledged the concerns of religious groups about the plans but said there need not be a choice "between religious belief and fairness for same sex couples".
But some MPs raised concerns that, by changing marriage from being solely between a man and a woman, fundamental parts of marriage, such as the ability to divorce on the grounds of adultery or failure to consummate the marriage, would not apply to same-sex marriages.
This is because current legal definitions of adultery and consummation are based on sexual contact between a man and a woman.
"There is absolutely no doubt that once marriage is re-defined in this very fundamental way, a whole number of new legal questions will arise, and no one can be quite sure what the outcome will be," warned Sir Tony Baldry, a Conservative MP and the Church of England's representative in the Commons.
"The government believes that this is a risk worth taking; the Church of England believes that it is not."
"Marriage is the union between a man and a woman, has been historically, remains so. It is Alice in Wonderland territory, Orwellian almost, for any government of any political persuasion to seek to come along and try to re-write the lexicon. It will not do", said Sir Roger Gale, the Conservative MP for Thanet North.
"There is a way forward. It's been suggested, but it's been ignored," he added.
"I don't subscribe to it myself, but I recognise the merit in the argument, and that is this: if the government is serious about this, take it away, abolish the Civil Partnerships Bill, abolish civil marriage, and create a Civil Union Bill that applies to all people irrespective of the sexuality, or their relationships, and that means brothers and brothers, and sisters and sisters, and brothers and sisters as well.
"That would be a way forward. This is not."
'Right side of history'
Reports suggest upwards of 120 Conservative MPs could vote against the government's plans, including some cabinet ministers.
MPs will have a free vote on the bill, meaning they will not be ordered to vote for or against by party whips.
The legislation is expected to pass through the Commons with most on the Labour and Liberal Democrat benches supporting it.
For Labour, Yvette Cooper called on MPs to back the proposals, saying: "Couples who love each other should be able to get married regardless of their gender and their sexuality."
She said she wanted to see same-sex relationships "celebrated and valued by the state in the same way as everyone else".
Ms Cooper argued that the bill would keep the institution of marriage "inclusive and in touch for the next generation".
"Let's celebrate not discriminate, and let's be on the right side of history, and vote for this bill today," she urged MPs.
On Tuesday, Chancellor George Osborne, Foreign Secretary William Hague and Home Secretary Theresa May wrote to the Daily Telegraph in an attempt to persuade Tory MPs to back the plan.
They wrote: "Marriage has evolved over time. We believe that opening it up to same-sex couples will strengthen, not weaken, the institution."
The government believes that the wording of the bill will ensure that the Church of England and the Church in Wales will not face any legal challenges to their strong stated opposition to holding same-sex marriages.
All religious organisations will be able to opt in to holding ceremonies - but the Church of England and the Church in Wales would first need to agree to change canon law.