"This is, yes, about equality. But it is also about making our society stronger.
"I know there are strong views on both sides of the argument - I accept that. But I think this is an important step forward for our country."
Mr Cameron was speaking as a stormy debate on the second reading of the Marriage (Same Sex Couples) Bill drew to its conclusion in the House of Commons.
Introducing the Bill, Culture Secretary Maria Miller insisted that it would make Britain "a fairer place to live".
But she faced opposition from numerous Tory MPs, including the chairman of the backbench 1922 Committee Graham Brady, who said he had "serious misgivings" over ministers' assurances that religious freedom will not be compromised.