MPs will vote on re-joining the European arrest warrant before the Rochester and Strood by-election, David Cameron has told MPs.
The Prime Minister made the announcement in response to claims by Ed Miliband that he was holding back on the vote because of the Ukip challenge in the seat.
But, speaking at Prime Minister's Questions, Mr Cameron said the delay was because the Spanish government was holding up negotiations.
Mr Miliband said the Prime Minister was "paralysed by fear" over a Tory rebellion and offered to use Labour's opposition day next week to stage the vote and help to get it through.
But Mr Cameron said: "There's only one problem with your question - which is we are going to have a vote, we are going to have it before the Rochester by-election.
"Your questions have just collapsed."
Mr Miliband used the subject to open his questions, and said: "A vital tool that has helped to bring murderers, rapists and paedophiles to justice is the European arrest warrant.
"Why are you delaying having a vote on it?"
Mr Cameron replied: "I'm not delaying having a vote on it, there will be a vote on it. We need in order to have a vote on it the small matter of a negotiation to take place within Europe which up to now the Spanish have been blocking.
"I think the Spanish will shortly remove their block and at that moment we will be able to have a vote."
Mr Miliband pressed the point and asked: "We all know the reason you are not having a vote - it's the by-election in Rochester and Strood.
"You are paralysed by fear of another backbench rebellion on Europe.
"So I want to make an offer to you: we have got a Labour opposition day next week. We will give you the time for a vote on the European arrest warrant and we will help you get it through."
Mr Cameron then made the pledge on a vote before the November 20 poll, prompting Mr Miliband to add: "All I can say is I look forward to us walking through the lobby together to vote for the European arrest warrant, two parties working together in the national interest - or maybe given your backbenchers one and a half parties working together in the national interest."
The Prime Minister added: "Let me add some detail on the vote on the European arrest warrant, because this is an important issue.
"What we have achieved with the justice and home affairs opt out is the biggest transfer of power from Brussels back to Britain as we have opted out of over 100 measures.
"But it is important we take action to keep Britain safe, particularly from serious criminals and terrorists, and the European arrest warrant offers the best way of doing that.
"I would stress to those who are concerned about this, the European arrest warrant is very different from the arrest warrant first introduced under the last Labour government.
"You cannot now be extradited for something that isn't a crime in Britain, judges are able to reject European arrest warrants and they have done so in many, many cases.
"And you can't be extradited if there is going to be a long period of detention. These are all important considerations."
Mr Cameron added: "I'm sure you are looking forward to walking through the lobbies with somebody because you've had rather a lonely week with the loss of your leader in Scotland, the total shambles in Yorkshire and all the other problems you have got."
Downing Street aides later said no date had yet been set for a Commons vote on the EAW - and the other 34 justice and home affairs measures which the UK wishes to retain - but that it would have to take place by December 1 to meet the re-adoption deadline.
A source said: "It will happen before the by-election. We are quite close. There's been a long negotiation and there is one particular part that is yet to fall into place."
The outstanding issue relates to Spain, which has being raising concerns relating to Gibraltar during the negotiation process.
Asked whether the Prime Minister was expecting a rebellion by Eurosceptic Tory backbenchers when the warrant comes to Parliament, the source replied: "Of course, we always want Conservative MPs to support Government policy and Government votes."
A Labour source said the offer to use opposition time next Wednesday to vote on the EAW was still on the table.
"We now need to have some more questions answered by the Government," said the source. "We strongly believe in retaining the EAW, which helps keep our communities safe and stops criminals fleeing justice.
"If Mr Cameron is not playing games about this important measure, we need to know when he will re-adopt it and in what form. Our offer of time next Wednesday remains open."
International Development Secretary Justine Greening said the Government was "happy" to put the EAW to a vote because it had secured a number of important reforms.
She told BBC Radio 4's World At One: "Chief constables are saying they need this in place and we're confident that this is actually an important measure to help us combat crime."
Asked if she was fully behind it, Ms Greening replied: " Yes."
Pressed on the potential for a massive Conservative rebellion when it goes to a vote, she said: "I think the reality is that when a lot of backbench Conservative MPs actually look at how the European Arrest Warrant has been reformed, how it will actually work in practice now, I believe that they will have the confidence to be able to support what is an important measure."
Shadow foreign secretary Douglas Alexander told the programme: "The truth is this issue has been delayed, not for reasons of policy but reasons of politics.
"There's a very significant number of Conservative backbenchers who frankly don't seem to care if the country would be left less safe if they have got an opportunity to vote against Europe."