The warrant will help secure extradition across the EU
Home Office minister Angela Eagle said the 14 other European Union countries might have to go ahead with the initiative without Italy if an agreement is not reached.
Her warning followed the collapse of talks to finalise arrangements for the warrant in Brussels on Friday.
The Italian delegation introduced last-minute amendments which would significantly water down the proposal.
The warrant is the basis of EU anti-terror measures proposed since the 11 September attacks.
"Fourteen countries made compromises in order to get agreement on the EU arrest warrant and then they [the Italians] brought up a lot of things that they hadn't given us any notice of," Ms Eagle told BBC Radio 4's Today programme.
"We would have been able to deal with them if they had stated them earlier, rather than waiting to the last minute to bring up a series of objections."
Hopeful
The proposed warrant - due to be introduced in Britain in an Extradition Bill in the New Year - would allow courts in any EU country to secure the arrest and extradition of people suspected of a range of 32 serious crimes, from terrorism to money-laundering and fraud.
The EU had been determined to push through the warrant quickly to face off criticism of its slow bureaucracy and show it could act quickly in the face of an international threat.
There are suspicions that Italy's objections are motivated by the personal concerns of its Prime Minister, Silvio Berlusconi, who has had run-ins with the judiciary over his business interests.
Ms Eagle refused to speculate on the Italians' motives, but said she was still hopeful of a deal with Rome.
She urged the Italians to look at the wider issues.
Last-ditch talks
"We want to get an agreement with them," she said.
"We have to realise that the European arrest warrant will actually help us fight serious crime and terrorism, which is globalised.
"It will update our extradition laws in the EU and give us the tools to be successful in that fight."
But she said going ahead without the Italians was an option that would be considered if agreement was not reached.
Belgian Prime Minister Guy Verhofstadt is to go to Rome next week to tackle Italian Prime Minister Silvio Berlusconi directly on the matter ahead of the leaders' summit in Laeken, where a decision on the warrant is expected.