Plans to remove the right of legal aid defendants in criminal cases in England and Wales to choose their solicitor have been scrapped.
Ministers planned to put the onus on lawyers competing for contracts but have said it now recognises choice is seen as "fundamental".
The Ministry of Justice said it was now "developing alternatives" to include competitive tendering and "some extent" of choice for defendants.
Labour called the move "embarrassing".
The plan to remove defendants' right to choose was part of the government's drive to cut £220m from the annual criminal case legal aid budget in England and Wales.
Other aspects of the scheme, such as a suggestion defendants with a disposable income of more than £37,500 should not get automatic access to legal aid, remain unchanged.
Legal aid costs taxpayers about £2bn every year and criminal defence makes up more than half of the expenditure, a situation which ministers say is unsustainable in the current financial climate.
The government wants to see fewer but bigger organisations providing legal aid as part of a streamlined system.
But the Bar Council has argued this would result in the end of the long-held right of a defendant to choose a legal aid solicitor and people would effectively be allocated a representative on the basis of cost.
A senior judge warned last month people with disabilities would not be able to choose a lawyer who understood their condition, and those involved in complex cases would not be able to seek out specialists.
An online petition against "depriving citizens of legal aid or the right to representation by the solicitor of their choice" received more than 100,000 signatures - the threshold required to be considered for a parliamentary debate.
Justice Secretary Chris Grayling said he was prepared to reconsider the original proposal as long as it still met the "core objectives" of his reforms to create a more cost-effective and efficient system.
"The rationale for proposing this change was to give greater certainty of case volume for providers, making it easier and more predictable for them to organise their businesses," he wrote in a letter to Commons Justice Committee chairman Sir Alan Beith.
"It is not a policy objective in its own right. However, I have heard clearly from the Law Society and other respondents that they regard client choice as fundamental to the effective delivery of criminal legal aid."
Mr Grayling said he was also prepared to consider arguments for a gradual consolidation of legal aid providers in order to preserve quality of representation and prevent "advice deserts" in certain areas.
He added: "I have made clear throughout that I am open to alternative proposals that meet the same objectives, including delivering the same level of savings."
But the justice secretary said his department's settlement in the recent Spending Review - which will see it have to make a further 10% cuts in 2015-16 - should "leave no-one in any doubt" about the need for savings in legal aid.
A Ministry of Justice spokesman said it was considering how to combine competitive tendering by law firms with "some extent" of choice for defendants.
Shadow justice minister Andy Slaughter said the decision on choice of legal aid solicitors was an "embarrassing U-turn" for the government.
The Law Society, which represents solicitors, welcomed the move.
"Client choice is important not just as a matter of principle but also as a matter of practicality," president Lucy Scott-Moncrieff told BBC Radio 4's Today programme.
"If people can choose their lawyer then lawyers will make every effort to attract work by doing their job as well as they can."
And the Bar Council said the concession was a "significant victory" for opponents of the government's wider proposals.
"We welcome the government's change of heart on this, but we hope it is also listening to the many voices which are clear that price competitive tendering in any form is not a suitable mechanism for allocating legal aid contracts," Maura McGowan QC, chairwoman of the council, said.
"Legal aid contracts should not just go to the bidders who are willing to do the work for the lowest price."