Chancellor George Osborne will “lessen” the impact of tax credit cuts on families after peers inflicted a serious blow on the government by demanding changes.
He promised “transitional help” for those affected after his party was defeated twice in the House of Lords.
But he vowed to press on with changes designed to save billions from welfare.
Downing Street has signalled a review of Lords conventions to address what it says are “constitutional issues”.
Conservative MPs reacted angrily to the defeats, accusing the House of Lords of over-stepping the mark in blocking measures backed by elected MPs.
Mr Osborne, facing MPs at Treasury questions, said: “We will continue to reform tax credits and save the money needed so that Britain lives within its means, while at the same time lessening the impact on families during the transition.”
He said he would set out the details of how he will do this his Autumn Statement at the end of November – he needs to find up to £4.4bn to cover the cost of the climb down.
He added: “We are as determined as ever to have a low tax, low welfare, high wage economy that Britain needs and the British people want to see.”
Tax credits were introduced by the last Labour government to help low-paid families. Under the government’s plans, the income threshold for receiving Working Tax Credits and Child Tax Credit is due to be cut from April.
Critics say the move could deprive low-income workers of up to £1,300 a year.
But the government says it is essential to tackle the deficit and argues most claimants will be better off when other changes, such as the introduction of the new national living wage, are taken into account.
During a dramatic evening in the House of Lords, peers voted by a majority of 17 to back Labour calls for the government to provide full financial redress to the millions of tax credit claimants who will be affected when their entitlements are reduced.
Peers inflicted a second defeat by backing a delay in the cuts until an assessment of their financial impact is carried out.
Analysis by the BBC’s political editor Laura Kuenssberg
Last night a slightly – and unusually – shaky-looking George Osborne said the Lords had behaved in an unconstitutional way and would be “dealt with”.
There is an unresolved question about how far the Lords should stray into the government’s finances. It’s very clear ministers want to put the problem at peers’ door, not their own.
On Tuesday, No 10 will announce some kind of review.
But the real problem is how on earth ministers, and particularly George Osborne, pull themselves out of a hole they have dug with their own hands.
However, they stopped short of blocking the changes entirely, by rejecting a so-called “fatal motion” tabled by the Liberal Democrats.
Mr Osborne responded by hinting at changes to the original proposals, which have been approved three times by MPs, in next month’s Autumn Statement.
“I have said I would listen and that’s precisely what I intend to do,” he said. “I believe we can achieve the same goal of reforming tax credits saving the money we need to save to secure our economy, while at the same time helping in the transition.
“That is what I intend to do in the Autumn Statement. I’m determined to deliver that lower welfare economy the British people want to see.”
Shadow chancellor John McDonnell said the policy was “unacceptable” to the public and called for Mr Osborne to make a statement to Parliament when he attends Treasury Questions on Tuesday.
“George Osborne has got to think again,” he told Sky News. “He has been defeated twice in the House of Lords tonight but there are a large number of Conservative MPs as well who have been telling him very, very clearly he has got to think again on this one.”
Fellow Labour MP Owen Smith, the party’s shadow work and pensions spokesman, said the Lords had “spoken for the country” and he urged Mr Osborne to come to the Commons immediately to tell MPs what he now plans to do, rather than keeping tax credit recipients “dangling” for a month until his Autumn Statement.
Tax credits are a series of benefits introduced by the last Labour government to help low-paid families. There are two types: Working Tax Credit (WTC) for those in work, and Child Tax Credit (CTC) for those with children.
Under the government’s original proposals, the income threshold for Working Tax Credits – £6,420 – will be cut to £3,850 a year from April.
In other words, as soon as someone earns £3,850, they will see their payments reduced. The income threshold for those only claiming CTCs will be cut from £16,105 to £12,125.
The rate at which those payments are cut is also going to get faster. Currently, for every £1 claimants earn above the threshold, they lose 41p. This is known as the taper rate. But from April, the taper rate will accelerate to 48p.
There will be similar reductions for those who claim work allowances under the new Universal Credit.
Heidi Allen, one of several Conservative MPs to express reservations about the policy, backed the pause saying it was “right that we delay changes to tax credits until we fully understand the impact”.
David Davis, another opponent, told BBC Radio 4’s Today programme “someone had to tell the government to think again”.
But other Tories called for the Lords to face “consequences”, claiming the unelected chamber had over-reached itself and flouted longstanding conventions giving the elected Commons the exclusive power to determine matters of taxation and government expenditure.
“Not for 100 years has the House of Lords defied this elected House,” Sir Edward Leigh said.
“This is a serious matter and I ask for the Commons Speaker to give a statement to protect the rights of the elected representatives, not just for us but for the people of this country.”
What the papers say
The government’s defeat in the Lords on Monday night makes the front pages of most newspapers.
The Daily Telegraph says the chancellor will reveal measures next month to “soften the impact of cuts”, while the Independent says Mr Osborne’s plan to find £12bn welfare savings is “in turmoil”.
The Guardian says David Cameron will outline a “rapid review” aimed at limiting the upper house’s powers, but the Mirror says Monday night’s votes were a “humiliation” for the prime minister.
Read the full paper review here.
Downing Street said a review of the constitutional implications would begin straight away, arguing that a “convention exists and it has been broken”.
Mr Osborne also said the matter would not be let to rest. “Tonight un-elected Labour and Liberal Lords have defeated a financial matter passed by the elected House of Commons.
“David Cameron and I are clear that this raises constitutional issues that need to be dealt with.”