Rows over MPs expenses have been going on for more than a year
The government has abandoned plans for a vote on scrapping MPs' second homes allowance, it has announced.
Gordon Brown's plan to replace it with a flat-rate daily allowance failed to win support from the Tories, Lib Dems and many backbench Labour MPs.
The prime minister said "swift reform" was still needed and asked standards watchdog Sir Christopher Kelly to bring forward his report on expenses to July.
But Sir Christopher warned that the issues involved were "not simple".
MPs will still vote on Thursday on other plans for reform put forward by the government.
'Soon as possible'
The Tories and Lib Dems have argued that an attendance allowance which does not require receipts is less transparent than the current system.
The independent inquiry by Sir Christopher's Committee on Standards in Public Life is due to report back by the end of this year.
I continue to highly value the role of the Committee on Standards in Public Life and look forward to your report on all aspects of MPs' allowances
In his letter to Sir Christopher, Mr Brown said: "The government remains determined to move to an allowance system that is fair, transparent and less costly than the current system."
He also said: "You will also be aware that a consensus has not been reached on the future of the Personal Additional Accommodation Expenditure for MPs. But we are agreed on the need for swift reform.
"Therefore I would ask the Committee on Standards in Public Life to come forward with its proposals on this issue as soon as possible and preferably before the summer recess, taking into account MPs' attendance at Westminster, the need for transparency and accountability and the desire to reduce the existing limits on the allowances which MPs may claim, producing overall cost savings."
He added: "I continue to highly value the role of the Committee on Standards in Public Life and look forward to your report on all aspects of MPs' allowances."
But in his reply, Sir Christopher said the issues were "not simple" and that "making recommendations based on evidence is key if we are to put forward a workable and credible package of changes".
He added: "We aim to complete our review as early as we can consistent with doing a thorough job."
BBC political correspondent Gary O'Donoghue said that "while the prime minister was trying to seize the initiative on expenses, he has ended up looking powerless".
"This is proving to be a frustrating episode for Gordon Brown," our correspondent said.
The Commons debate and vote on Thursday will now concentrate on other proposals made by Mr Brown last week.
These include increasing transparency around MPs' outside earnings and ending claims for second homes from MPs with constituencies in greater London from 2010.
The government also wants MPs to provide receipts to support all expenses claims by removing the current £25 lower threshold.
Mr Brown proposes giving a senior group of MPs, the Members Estimate Committee, the power to amend the Green Book governing rules on MPs' expenses.
MPs' staff should be centrally employed by the House of Commons itself, rather than individual members, he added in his letter.
Conservative leader David Cameron said: "What we've seen from the prime minister is a U-turn, followed by a climbdown, and now descending into farce.
"He is ducking the issue which people want dealt with, which is a cleaned up system of expenses so we stop the business of MPs claiming for televisions, patio heaters and the rest of it."
Liberal Democrat leader Nick Clegg said: "This leaves us with the worst of both worlds.
"The most important issue of all has been kicked into the long grass, while Parliament will be left discussing other relatively minor issues.
"Gordon Brown didn't get his way with his proposal to pay MPs for turning up so he is denying us any chance to debate the issue of second homes. It's like a sulking child packing up his bat and ball and going home."
Mr Brown's plan to replace the controversial second homes allowance - worth up to £24,000 a year to MPs representing seats outside inner London - failed to win support among opposition parties.
It came as a surprise to many when it was announced on the Downing Street website last week.
But it was quickly criticised by the Tories and Liberal Democrats, who said a "clocking on" allowance amounted to a "cheque for turning up to work" and was much criticised where it operated in the European Parliament.
Sir Christopher also said people would have "great difficulty in the notion that claims for the reimbursement of expenses should not need to be backed by receipts".
Asked on Monday if the plan for a flat-rate allowance was dead, Commons leader Harriet Harman said: "No, not at all."
In July all MPs' expenses claims, with receipts, dating back to 2004 are due to be published after a long freedom of information battle.