Chancellor Alistair Darling has been accused of incompetency by the Conservatives
The chancellor has admitted "it will take time" to finalise compensation details for people who lost out when the 10p income tax rate was scrapped.
Alistair Darling told MPs he would wait until this autumn's pre-Budget report to outline the package, as changes to the tax system "can be quite complex".
Concessions were offered to some low earners and pensioners under 65 amid fears of a rebellion by Labour MPs.
Conservative leader David Cameron said the affair was "a complete shambles".
"Even when it comes to making a U-turn, this government is incompetent," he added.
"With this prime minister and with this chancellor you have always got to check the smallprint."
The abolition of the 10p rate was part of Gordon Brown's final Budget as chancellor, before he became prime minister last year, and came into effect earlier this month.
The support package, announced by Mr Darling on Wednesday, will be given to some people who have lost out because of the change.
Groups such as low-paid workers without children and pensioners under 65 will be compensated through the winter-fuel allowance system, tax credits and the minimum wage, the chancellor said.
Mr Darling told MPs at Treasury questions that he expected to announce his plans to support those aged 60 to 64 "in the very near future".
This would "almost certainly" be done through winter-fuel payments, "because it's there and you don't need to legislate for anything different".
He added: "In the Budget I did increase the amount of money going to people over the age of 60 by Ŗ50 for this year, over and above the winter fuel payment."
"That was partly to reflect the fact that... people over the age of 60 are often on fixed incomes and that will help them," he added. "Those payments will go out in the autumn."
The chancellor stressed that "in relation to everybody else who's affected", there were "certain areas that I wanted to look at in relation to tax credits [and] the national minimum wage".
"I said that I would be setting out proposals and return to it at the pre-Budget report.
"That's what I said at the weekend; that's what I said in the letter to the Treasury select committee, and the letter set out quite clearly how I intend to proceed."
'Classic Gordon Brown'
Earlier the Conservatives called on the government to clarify whether all, or only some, of the package would be backdated to the start of April.
George Osborne, the shadow chancellor, described the affair as being "absolutely classic Gordon Brown".
"Even the U-turn, when you look at the detail, is not quite what it's made out to be," he said.
Liberal Democrat leader Nick Clegg called on the government to adopt a more radical approach.
He told BBC Radio 5 Live: "They doubled the 10p rate in order to make a sort of headline-grabbing announcement on lowering the 22p rate to 20p."
In doing so, he said, ministers "didn't understand the knock-on consequences of the lowest earners".
Following Mr Darling's announcement of concessions, Labour MP Frank Field immediately withdrew an amendment to the Finance Bill, calling for compensation, which had won the backing of 45 Labour MPs.
This level of support would have been sufficient to inflict Mr Brown's first defeat as prime minister if a vote had been held in the Commons.
One of the amendment's backers, Labour MP Ian Gibson, accused Mr Field of giving in too early.
"Of course when you make a deal with anybody, as every trade unionist knows, you don't take the first offer," he told BBC Radio 5 Live.
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The logic of compensating people by running them through a bureaucratic, means-tested system is baffling
"And secondly before you take away amendments, you should actually make sure you've got the details of the deal and you talk to your other members who've supported you."
But Mr Field said: "Even if the government wanted to - and the government doesn't want to - go back on this... the House will force through this package."
Tony Lloyd, who chairs the Parliamentary Labour Party, which comprises all Labour MPs, said the way the issue had been "resolved" was "exactly what ought to happen in a parliamentary democracy".
He said Labour MPs had passed on criticism from party workers and constituents, and "the government itself has listened and policy has changed in accordance with that".
"A listening government is a government that knows when it does have to change because it's in the wrong position," he told BBC Radio 4's The World at One.