Vince Cable has "every reason to be apologetic" over comments suggesting he may quit and bring the government down, David Cameron has said.
The business secretary was recorded saying serving in the coalition was like "fighting a war", likening some policies to a "Maoist revolution".
But the prime minister said he "got on" with Mr Cable, who was "embarrassed".
Labour said the comments showed the government was "paralysed" by strains between the Tories and Lib Dems.
The Daily Telegraph reports that Mr Cable - one of the most senior Lib Dems in the cabinet - said he could "bring the government down" if he resigned, adding that this remained a "nuclear option" of last resort.
'Get on well'
He was recorded telling the two female reporters, who were posing as voters at a constituency surgery, that he had been involved in a "big argument" with "our Conservative friends" over dealing with the bank bonuses and regulation.
He added: "If they push me too far then I can walk out and bring the government down and they know that."
The business secretary also criticised the speed at which the coalition was trying to push through changes in the health service, local government and other areas, which he described as a "kind of Maoist revolution", and said it was "in danger of getting out of control".
The axing of child benefit for higher earners had been carried out in a "rather cack-handed way", Mr Cable said.
At a joint Downing Street press conference with Deputy Prime Minister Nick Clegg, Mr Cameron said: "What he said was obviously wrong. He's apologised for that. He was very apologetic at cabinet this morning and we should leave it at that.
"He has every reason to be apologetic. But in a coalition you do have private disagreements on policy. If we all agreed we would be in the same party and we're not. We have to work these things out."
He added: "Personally, I get on with Vince very well. After cabinet we had a discussion about some other issues we were resolving between us."
Mr Cameron also said: "I find him a perfectly reasonable colleague to work with."
Mr Clegg announced that security at Mr Cable's constituency surgeries would be tightened up, telling reporters: "As far as Vince is concerned, he's embarrassed by what's happened and he's right to be embarrassed.
"My view and his view is that coalition government can only work effectively if disagreements, where they exist, are thrashed out in private and we come to a common solution."
Questioned about Mr Cable's description of some of the administration's agenda as "Maoist", Mr Clegg said: "I fully disagree with Vince on that."
In a statement following the Telegraph's revelations, Mr Cable said: "Naturally I am embarrassed by these comments and I regret them.
"I have no intention of leaving the government. I am proud of what it is achieving and will continue to play my full part in delivering the priorities I and my party believe in, which are enshrined in the coalition agreement."
At a robust Commons Treasury questions session earlier on Tuesday, Labour's shadow chancellor, Alan Johnson, asked George Osborne: "Does the chancellor recognise himself in the business secretary's description of 'cack-handed Tories'?"
Mr Osborne replied: "The business secretary is a powerful ally in the government and in promoting growth and, frankly, he's forgotten more about economics than the shadow chancellor ever knew."
The BBC understands that several other leading Lib Dems, including health minister Paul Burstow, have also been approached by undercover reporters.