MPs are to be given a vote on whether to stage a full judicial inquiry into the banking scandal, the Government announced tonight.
The Leader of the Commons Sir George Young said there would be a debate on Thursday on whether a judge should investigate, or whether it should be dealt with by a committee of MPs and peers.
David Cameron announced on Monday that the Government intended to set up a joint, cross-party committee of the Commons and Lords to carry out an inquiry into rate-rigging by the banks.
However the plan immediately ran into trouble after Labour insisted only a judicial inquiry - along the lines of the Leveson Inquiry into the media - could get to the bottom of the problem.
The man chosen by the Government to chair the joint committee - the chairman of the Commons Treasury Committee, Tory MP Andrew Tyrie - then said he was not prepared to go ahead unless there was a cross-party consensus.
Other MPs on the Treasury Committee were said to be unhappy that a joint committee inquiry would cut across its inquiry into bank governance which was already under way.
Downing Street insisted ministers wanted to work with the opposition, but Labour reacted with fury after Government sources were quoted, accusing the party of trying to avoid a rapid parliamentary inquiry in order to "save Ed Balls' skin".
Chancellor George Osborne had earlier stoked tensions, saying he would like to see the shadow chancellor - who was City minister in the Labour government during part of the time of the Libor scandal - "in the dock".
In the Commons on Monday, Mr Osborne had taunted Mr Balls, saying: "Put your hand up if you were the City minister when the Libor scandal happened."
No 10 insisted it should still be possible for a joint committee to proceed on a non-partisan basis, disclosing that Mr Cameron had spoken to Labour leader Ed Miliband before announcing the Government's proposals.
"I am sure there will be political points made about some of these issues. Some of these issues have been debated in the past between political parties," the Prime Minister's official spokesman said.
"We certainly want to see this inquiry address them in a way that has cross-party support."
However Mr Balls said the Government had destroyed trust in its ability to approach the issue in a non-party political manner.
"The way the Government has handled this since yesterday in a totally partisan way is, to be honest, undermining trust," he told Sky News's Boulton & Co.
"My fear is us co-operating in a parliamentary inquiry would be third best, it wouldn't satisfy the public. So I would much prefer that we don't go down that road."
Sir George acknowledged that - with the main parties divided - the only way to resolve the issue was to put the two alternative proposals to a Commons vote.
"There is a disagreement between the two sides as to the best way forward," he told MPs in an emergency business statement.
"I think the right way to resolve that disagreement is to have a debate and then have a vote on the two alternative propositions. That is how this House makes a decision."
Nevertheless it was unclear whether, even if the Government won the vote, Mr Tyrie would consider there was sufficient cross-party consensus for him to proceed.
Sir George said: "I very much hope that in the debate that we have on Thursday, members of the Treasury Select Committee, including possibly the chair of that committee, may put forward their views on the proposition we have put forward before the House."
Ministers argue that a rapid, tightly-focused parliamentary inquiry is the best way to bring forward recommendations in time for inclusion in the Government's planned banking reform bill to be published next year.
"What I want to see is recommendations made quickly so that we can get on and implement them, which is, I think, what the people of this country want to see," said Treasury Chief Secretary Danny Alexander.
"I hope that Labour aren't arguing for an alternative, longer timescale inquiry on the basis that they want a smokescreen to protect their own position."
However Mr Miliband warned that an inquiry by parliamentarians would lack credibility with the public.
"I have to say to David Cameron that if he doesn't order a judge-led inquiry, I think he will be failing to understand the gravity and scale of this crisis," Mr Miliband said.
"The last thing the public want is a sense that the establishment is trying to cover this up and sweep it under the carpet."