Mr Cameron admitted the actions of some MPs had damaged the party
MPs who claimed for "phantom" mortgages on expenses should be investigated by the police and prosecuted if warranted, Tory leader David Cameron has said.
His call came as Labour's Elliot Morley became the latest MP to announce he would stand down at the next election.
Mr Morley has apologised for mortgage interest payment claims but said he had made a "genuine mistake".
Mr Cameron said MPs who had committed a crime with their expenses claims should "face the full force of the law".
Thirteen MPs have announced their intention to stand down since details of expenses claims have been published.
Meanwhile, a new opinion poll has suggested that Labour is being badly damaged by the expenses scandal in the run-up to next week's European elections.
'Force of law'
Mr Morley had claimed for mortgage interest payments of £16,000 - 18 months after the mortgage was paid off.
He has apologised and repaid the money, blaming "sloppy accounting".
Campaigners for Mr Morley to stand down are calling for him to quit his post immediately, rather than waiting until the next general election.
A statement on the elliotmustgo.com website said: "He has already lost all credibility with his constituents, the media and local businesses and will continue to do so while he remains in office."
Two other Labour MPs - David Chaytor and Ben Chapman - have also admitted "errors" in claiming for mortgages that had already been paid off.
And Tory MP Bill Wiggin blamed the Commons Fees Office for not correcting his repeated "mistake" when he claimed for a mortgage on his constituency home rather than his London second home.
Scotland Yard is currently considering whether to launch criminal inquiries into any potentially fraudulent claims.
In an interview with the Daily Telegraph, Mr Cameron said: "If people have broken the law in claiming expenses, like mortgage payments for mortgages that don't exist, should they be subject to the full force of the law? Yes of course they should.
"I've said it's not for me to call in the police but the police know what the law is and if they feel it's been broken they should be able to look at that without fear or favour."
Liberal Democrat MP Susan Kramer said an early general election was needed to restore public trust.
She told BBC News: "What do we do if we've got votes or debates in the coming months and we've got MPs who in effect have been deselected, either by the local parties or, in effect, because of the views of their constituents; are they going to speak in debates? Are they going to be part of votes?
"I don't see how we've got any integrity in the system until we can clean this whole thing out."
Mr Morley made his announcement about stepping down on Friday night, following a meeting with local Labour Party officials in his Scunthorpe constituency.
He said the pressure had been affecting his family and his health and insisted the decision was his own.
In a statement the former farming minister said the last two weeks had been "traumatic".
Mr Morley added that he had made a "genuine mistake" and insisted that he believed he would be cleared of any wrong-doing.
The latest MPs named in the Telegraph on Saturday include Tory frontbencher Eleanor Lang, who told the paper that she was not obliged to pay capital gains tax on the profit she made from the sale of her second home, because it was within the rules.
The paper also criticised Tory MP Humfrey Malins for letting his children stay rent-free in his taxpayer-funded second home in London.
He denied claims he did not live in the flat, saying he spent an average of two nights a week there. He said his daughter had stayed there "for some periods", with his son an "infrequent visitor" - neither of which had cost the taxpayer "a penny".
He said he believed his conduct had been "perfectly proper throughout".
Meanwhile a Populus poll in Saturday's Times newspaper provides gloomy reading for Prime Minister Gordon Brown, with Labour is at its lowest ever national rating following the expenses expose.
According to the poll, carried out on 26-27 May on a sample of 1,001 adults, Labour trailed in third place after the UK Independence Party with just 16% of respondents prepared to vote for them in next week's European elections.
BBC political editor Nick Robinson said: "If that [projection] was to be repeated in next Sunday's results, it would have serious consequences for Gordon Brown and raise serious questions over how and whether he can help his party recover."
UKIP's leader, Nigel Farage, told BBC News: "What I would really like to see if is UKIP can cause an earthquake next Thursday, if we can really send a loud and clear message to the big party leaders."