The House of Lords vote to block tax credit cuts creates a "big constitutional issue", leader of House of Commons Chris Grayling has said.
The former Conservative Justice Secretary said it "cannot be right" for the unelected Lords to stand in the way of the changes.
Mr Grayling told Good Morning Britain: "Of course it's a difficult decision to have to take but we have a big task still ahead of us to balance the nation's books and create a sound financial foundation for the next generation.
"What shouldn't happen is unelected peers breaking the traditions of decades and throwing out a financial measure in the wake of three votes in the House of Commons which said we need to go ahead with this."
Mr Grayling said the tax credit cuts were part of a package of changes, including free childcare and cuts to social rents, designed to help working families.
Chancellor George Osborne has vowed to take on the House of Lords after peers dealt a devastating blow to plans to cut tax credits.
The vote - the first time in 100 years the Lords has defied the elected Commons on a financial matter - saw a motion to delay the £4.4 billion of cuts while an impact assessment is carried out win by 307 votes to 277.
A second motion to delay the cuts by at least three years was also passed, by 289 votes to 272.
Mr Osborne said both he and Prime Minister David Cameron were "clear" that the rebellion would "need to be dealt with".
"It has happened, and now we must address the consequences of that. I said I would listen and that's precisely what I intend to do," he added.
"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."
A Number 10 spokesman said now that the century-old agreement between the Commons and the Lords had been broken, Mr Cameron had ordered a "rapid review" to try to "see how it can be put back in place".
By the end of the year, Britain will have a £69.5bn deficit.
The proposed cuts to tax credits would have saved £4.4bn so how will George Osborne plug that gap now?
ITV News At Ten Presenter Tom Bradby reports:
George Osborne has been forced to rethink his plans for tax credit cuts after an "embarrassing" defeat in the House of Lords.
The Chancellor now has a month to come up with a Plan B when he delivers his Autumn statement.
ITV News Deputy Political Editor Chris Ship reports:
George Osborne has said he remains "determined to deliver" the government's economic reforms, despite the defeat dealt to his planned tax credit cuts in the House of Lords.
Speaking to ITV News, the chancellor said he would set out transitional arrangements to help people hit by tax credit cuts in the Autumn Statement.
He also warned that he and Prime Minister David Cameron saw the defeat as raising "constitutional issues that need to be dealt with".
There were cheers in the House of Commons tonight as proceedings were interrupted to announce peers had voted against the government on tax credit cuts.
The historic moment is the first time in 100 years the House of Lords has defied the elected house.
David Cameron said the move has created a "constitutional issue" which must be resolved.
Labour's Shadow Chancellor has said the Tories are in "utter disarray" after being defeated over tax credit cuts in the House of Lords.
John McDonnell said: "George Osborne needs to now go away, and consider the only reasonable option open to him.
"If he u-turns fairly and in full on his tax credit cuts then I will support him on it, and so will the public.
"But if he continues down his path of tax cuts for for the rich paid for by tax credit cuts for many hardworking families, then he will be putting the interests of his party before the interests of those working families who just want to pay their bills and get to the end of each month."
David Cameron has called for a "rapid review" on the constitution of the House of Lords after they voted against the government for the first time in 100 years.
The Prime Minister's plans to cut tax credits have now been delayed after two motions were passed by peers.
A Number 10 spokesman said: "The Prime Minister is determined we will address this constitutional issue.
"A convention exists and it has been broken. He has asked for a rapid review to see how it can be put back in place."
Peers have voted to delay tax credit cuts for at least three years under proposals put forward by Labour's Baroness Hollis.
It is another defeat for the government after Lords voted to delay the changes until plans an assessment is done on how it will impact the low paid.
ITV News Deputy Political Editor Chris Ship tweeted:
Wow. Big moment in Lords. Labour's Baroness Hollis motion: Contents 289 Not Contents 272. Government DEFEAT