PM David Cameron has "struck exactly the right note on migration", Education Secretary Michael Gove has said.
The Sunday Times reports that Mr Cameron wants to quadruple the period that EU migrants need to have spent in the UK before they qualify for benefits from three months to a year.
But a Lib Dem cabinet minister has suggested that this could put the UK on the wrong side of the argument.
Restrictions on migration from Bulgaria and Romania are set to end in 2014.
Mr Gove was asked on BBC1's Andrew Marr show about the Sunday Times report, which said the PM was "preparing for a showdown" with the EU over the issue.
The education secretary replied: "I absolutely agree with him and I do think it's practical politics."
Mr Cameron had "struck exactly the right note on migration, which is to celebrate the achievements of the people who've come here, to recognise migration has to work for people who are already here - from whatever background", he said.
"But when it comes to new migrants from accession countries in the EU we need to look properly at the benefits system here to make sure that people are coming here to work and to contribute - not to take advantage of what is rightly a generous welfare state."
The Lib Dem MP and Scottish Secretary Alistair Carmichael said told BBC Radio 5 Live's Peinaar's Politics that he would "need to be persuaded" that this was the best way forward.
"I can understand the concern and I can see the need for robust transitional arrangements," he said.
But he warned: "Potentially it might put us on the wrong side of the rest of the European Union.
"As a member state I don't particularly want to find myself in that territory.
For Labour, shadow home secretary Yvette Cooper admitted that the previous government had made mistakes over immigration controls.
She told the Andrew Marr show: "I do think when people are coming to this country, they should be contributing and so we've already said there are changes you could make to Jobseekers' Allowance so people can't come and claim Jobseekers' Allowance straight away.
"If the government had done that nine months ago, when we suggested it, you could have had more progress made on this right now."
But she added: "It's important to recognise that most people who come to this country do come to work and to contribute."