Home Secretary Theresa May says she will argue "loudly and clearly" in favour of rejoining the European Arrest Warrant (EAW) in a Commons debate.
David Cameron is facing a backbench rebellion when MPs vote on rejoining the EAW and 34 other EU measures.
Supporters of the EAW say Britain risks becoming a "safe haven" for criminals without its extradition powers.
But some Conservative MPs see it as a threat to the liberties of Britons and the sovereignty of the UK.
The government opted out of all 133 justice measures in 2013 and wants to rejoin 35, including the EAW.
It has until 1 December to decide which ones to continue to adhere to.
Writing in the Sunday Times, Conservative backbencher David Davis said claims by Mrs May and senior judges that without the EAW Britain would become a safe haven for criminals were "scaremongering".
He is among the MPs expected to vote against the government plans on Monday, but the measures are likely to pass with Labour and Liberal Democrat support.
In an article in the Sunday Telegraph, Mrs May urged the Commons to give the authorities "the powers they need to keep us safe".
In the past five years, she said, 5,000 people had been extradited from the UK under the EAW, including suspects wanted for 124 murders and 100 rapes.
But Conservative MEP Daniel Hannan disagreed, telling the BBC's Sunday Politics: "I know the security services want it, of course it makes life easier for them.
"But a state in which we automatically do what the police want is a police state and the role of politicians is to weigh the convenience of the police against the freedom of the subject."
European Arrest Warrants
- The European Arrest Warrant operates EU-wide and replaced separate extradition arrangements between the EU member states
- It was introduced in January 2004, and was prompted by the international anti-terror drive after the 11 September 2001 attacks on the United States
- A national judicial authority, such as a court, can issue an EU warrant to get a suspect extradited
- For a warrant to be valid, the suspect must be accused of an offence incurring a maximum penalty of at least a year in prison, or must have been already sentenced to at least four months in prison
Mr Hannan cited the case of five-year-old brain tumour patient Ashya King, whose parents were arrested in Spain after he was taken from hospital against medical advice, as an example of the "disproportionate" use of an EAW.
Meanwhile, the chairs of three influential Parliamentary committees accused the government of a "cavalier approach" to the debate.
The European Scrutiny, Justice and Home Affairs said Monday's vote had "no direct relevance" to the EAW and would not allow MPs to make any changes.
The committees have previously called for an individual motion on each of the 35 measures, rather than one vote on the whole package.
Home Affairs chairman Keith Vaz said: "Members of the House are expecting a separate vote on whether or not to rejoin the European Arrest Warrant.
"Monday's debate, on an unamendable, take-it-or-leave-it package, will not give us that opportunity."
Labour's shadow home secretary Yvette Cooper said Prime Minister David Cameron was "running scared" of a rebellion by not including the EAW in the package to be voted on.
She said: "We need the European Arrest Warrant and we should vote for it. All this tricky game playing means it's no wonder people don't trust David Cameron on Europe."
In a letter to Mrs Cooper, Mrs May wrote: "I shall be making very clear in the House on Monday - and am happy to do so now - that Monday's vote is a vote on the entire package of 35 measures."
She said: "The package includes the arrest warrant and other tools which are vitally important to our police and law enforcement agencies.
"It helps us to tackle cross-border crimes, deport foreign criminals, track down those who seek to evade the law, and bring them to justice.
"We are proud to bring it before Parliament on Monday as a package of measures which are in the national interest, but if Parliament rejects it, we will not join them.
"The government will be arguing loudly and clearly why it is so important that we do so."