Vince Cable and David Laws have joined Lib Dem leader Nick Clegg to apologise for breaking their party's pledge to oppose increasing student tuition fees.
In a party political broadcast to be aired next week, Mr Clegg will say he is sorry the party "did not stick" to its pre-election promise.
Business Secretary Vince Cable told the BBC it had been an "unwise commitment".
Labour said it was not good enough to "just brush that promise aside" after breaking a key election pledge.
Mr Clegg does not apologise for backing the decision to raise fees.
He continues to argue it was the right move in the circumstances and the package offered by the coalition - in which no fees are paid upfront - was fairer for students than the previous system of university finance.
The BBC's political editor Nick Robinson said some of Mr Clegg's aides had advised against the apology but the leadership hoped the admission would demonstrate that the party had learnt from its mistakes and "grown up".
MPs approved plans in 2010 to allow universities in England to charge annual tuition fees of up to £9,000, nearly three times the previous £3,200 limit.
Before the 2010 election, all Lib Dems had said they would oppose any rise in fees.
More than 21 Lib Dem MPs voted against the proposals at the time, including former leaders Charles Kennedy and Sir Menzies Campbell, while a further eight abstained or did not vote.
Mr Clegg was among 27 Lib Dems to support the proposals.
In next week's broadcast, filmed in Mr Clegg's home, the deputy prime minister returns to an issue which has been the source of the biggest division in the party since it came to power in May 2010.
"There's no easy way to say this: we made a pledge, we didn't stick to it - and for that I am sorry," he says.
"When you've made a mistake you should apologise. But more importantly - most important of all - you've got to learn from your mistakes. And that's what we will do.
"I will never again make a pledge unless as a party we are absolutely clear about how we can keep it."
Speaking to the BBC in 2010, Mr Clegg said he was "not going to apologise for this for one minute", adding that "to govern is to choose particularly when there is not very much money".
Harriet Harman, deputy leader of Labour, said: "This was not just the small print of his manifesto, this was Nick Clegg's key election promise when he asked people to vote for his party. It is not good enough for him to just brush that promise aside.
"Instead of crying crocodile tears he should vote with Labour to bring these tuition fees down. If Nick Clegg does not back his words with action he is just weak and spineless."
Mr Cable admitted that many voters had been angered by the rise in tuition fees, but he insisted the policy was being reappraised now students realised they didn't have to pay upfront.
"I was sceptical about the pledge but we agreed collectively to do it and I take my share of the responsibility," he said. "I signed the pledge on the basis that had we been in government on our own, which was the commitment, we would have put through that policy and we would have done so.
"It was an unwise commitment to have made and we regret that and that was the basis of the apology."
Education minister David Laws told Radio 4's Today it would have been "technically possible" to keep the fees pledge and ultimately scrap them but only if the Lib Dems had been governing on their own and ditched other key commitments such as support for disadvantaged pupils and tax breaks for the low paid.
Mr Laws said all Lib Dem MPs bore a "collective responsibility" but denied it was failure of leadership on Mr Clegg's part, pointing out that the party had keep its pledges on a range of other "big and important" issues.
But two days before the start of the Lib Dem autumn conference, a former adviser to the deputy prime minister said the party must decide whether to "back or sack" Mr Clegg and recent speculation about his future had to end.
Writing in the New Statesman, Richard Reeves said: "The mutterings have been growing louder for months, certainly since another bruising round of local election results in the spring.
"The question of Clegg's leadership has to be addressed. Indeed, given the party's current position, it would be irresponsible not to do so.
"Cards on the table: I think the party must stick with Clegg, and that Clegg must stick with both liberalism and coalition."