Cable said he had no knowledge of the 'reprehensible' polls leaked by Lord Oakeshott on Nick Clegg's leadership.
The Liberal Democrat peer is taking a leave of absence from the Lords and resigning from the party, but is he the 'busted flush' some think?
Read the full statement from Lord Oakeshott on why he is resigning from the Liberal Democrats.
By Chris Ship, ITV News Deputy Political Editor
Within the Liberal Democrats, Nick Clegg personally is pretty safe. His chief potential rivals - Vince Cable, Tim Farron and perhaps Danny Alexander - have all had to row in behind Mr Clegg and say how much they support him.
Where does it leave the Liberal Democrats in the country after the terrible showing in the local and European elections last week?
I don't think they are in a very good place at all.
David Cameron has said that he only judges Vince Cable by "the results he delivers", as he does all his ministers.
The Prime Minister was speaking in the wake of a failed leadership coup against his Liberal Democrat Deputy PM Nick Clegg.
Liberal Democrat leader Nick Clegg has said that he will not sack his Business Secretary after insisting that he had no part in a failed plot to oust him.
The Deputy Prime Minister said the Business Secretary was fully supportive of his leadership and insisted he did not believe "for a second" the Cabinet minister had been behind the plot to force him out of the party's top job.
During his regular Call Clegg show on LBC he said: "He was absolutely not aware of polls elsewhere. He has made it very, very clear that he, for instance, didn't want any questions about leadership in the poll which he did have some control over in his own constituency.
Nick Clegg has played down suggestions that Vince Cable knew about a controversial poll commissioned by Lord Oakeshott in the Deputy Prime Minister's constituency.
The peer, who has now resigned from the Liberal Democrats, privately commissioned surveys in several constituencies that showed a collapse in support for the party since 2010.
But Mr Clegg insisted the Business Secretary, once seen as an ally of Lord Oakeshott, was unaware of a survey in the Lib Dem leader's Sheffield Hallam seat.
"Vince Cable clearly didn't know a thing about a poll being conducted in Sheffield," the Deputy Prime Minister told BBC Radio Sheffield.
Vince Cable has insisted he has remained loyal to Nick Clegg, saying "there was no disloyalty whatever".
Speaking to the BBC in China the Business Secretary denied he was involved in secret polls undermining Mr Clegg's leadership, and said he wanted to make it "absolutely clear" he was backing the Deputy Prime Minister.
He added: "People are putting round the story that there is some division on that, there is not. I made it absolutely clear from the beginning of this week that there is absolutely no leadership issue."
He said that although "lots of polls" were carried out, he "knew nothing" about the ones that Lord Oakeshott ran, which indicated the party's general election performance would improve were Mr Clegg to resign.
Lord Oakeshott has since resigned from the Liberal Democrat party.
Nick Clegg has questioned Ukip's political intentions, saying that their leader Nigel Farage was "ploughing on with a politics of blame."
Speaking on LBC Radio's 'Call Clegg' programme, the deputy Prime Minister said that he felt Ukip's proposals would "only make feelings of insecurity worse."
Clegg is facing questions from the general public for the first time since the Liberal Democrats suffered a mauling in recent elections.
Nick Clegg will face further questions over his leadership of the Liberal Democrat despite facing down a failed coup from within his party earlier this week.
Clegg faces a potentially tricky situation in dealing with senior colleague Vince Cable, with the Business Secretary being forced to deny involvement in polls Lord Oakeshott ran which indicated the party's general election performance would improve were Mr Clegg to resign.
The Deputy Prime Minister will also face questions from the public for the first time since last weeks' poor election results on his weekly radio phone-in on LBC Radio.
Liberal Democrat Transport Minister Baroness Kramer has defended Vince Cable.
She told BBC Two's Newsnight:
All I can say is Vince has made a categorical statement, I'm comfortable with that.
He said that basically (Lord Oakeshott's) behaviour has been inexcusable.
As far as I'm concerned he's doing what he should do, which is he's in China working for the British economy and state.
Asked whether Dr Cable knew that Lord Oakeshott's polls were asking about the Business Secretary's suitability as a potential Lib Dem leader, Lady Kramer said:
I haven't talked to Vince.
Knowing Vince I very much doubt it because you just look at the statements that Vince made before he left for China, he was very supportive of Nick Clegg, he understands what our job is for the next year, he's made those same kind of statements in China.
Business Secretary Vince Cable said he had "absolutely no knowledge" of the polls conducted by Lord Oakeshott on the future of Vince Cable as Liberal Democrat party leader.
In his resignation statement, Lord Oakeshott said Vince Cable was aware of the results of the polls, and aware he was carrying them out.
Vince Cable said he was aware of some polls, intended for the purposes of planning for next year's general election, but not any of the polls in Inverness or Sheffield Hallam, concerning Nick Clegg's tenure. Speaking from China he said he regretted the resignation of his friend.