Fulfilling a long-standing pledge by his Conservative party to "recognise marriage in the tax system", Cameron has proposed married couples in which neither spouse is a higher-rate taxpayer should get breaks worth up to 200 pounds ($320) a year.
If approved by parliament, the measure will come into force in April 2015, just one month before the next national election. It is expected to benefit around 4 million couples.
"All we're saying is that marriage is a good thing for our country - it's the ultimate form of commitment under the law - and we want to show our support for it," Cameron wrote in an article published in Saturday's Daily Mail newspaper.
The measure will also apply to same-sex couples in civil partnerships. From next year, same-sex couples will be able to marry under a new law passed by parliament in July.
"This summer I was proud to make equal marriage the law. Love is love, commitment is commitment," Cameron wrote.
The main opposition Labour party said the measure would benefit a minority of married couples to the detriment of other groups, and any benefit was outweighed by a range of welfare benefit cuts introduced by Cameron's government since 2010.
"He's so out of touch he thinks people will get married for 3.85 pounds a week," lawmaker Rachel Reeves said for the party.
Labour's deputy leader Harriet Harman took to Twitter to denounce possible consequences of Cameron's plan. "Married man's tax allowance will go to man on his third wife but not to first two wives looking after his children!" she tweeted.
A campaign group called Don't Judge My Family said the plan discriminated against widows and widowers, single parents, the one in four children whom it said grow up in single parent families, and unmarried cohabiting couples, among other groups.
"It's about promoting a fantasy 1950s family and won't go to many of the families who need support the most. In these tough times the government should be helping families, not judging them," the group said on its website.
The Conservatives' junior coalition partners, the Liberal Democrats, said the measure was "the wrong priority".
"You don't build a fairer society by using the tax system to favour one type of family over another," said Lib Dem treasury spokesman Stephen Williams.
"It is also not clear to me why a single person should pay more tax on their income than someone who is married," he said.
Under the coalition agreement signed by the Conservatives and Lib Dems in 2010, Lib Dem lawmakers will be able to abstain on a bill introducing the measure without breaking the alliance. ($1 = 0.6203 British pounds)