Mr Brown is trying to win over Labour backbenchers
Gordon Brown has told Labour MPs he understands their concerns about the abolition of the 10p tax rate.
He is trying to head off a backbench rebellion by MPs angry that millions of low earners have been left worse off after changes in last year's Budget.
The PM told the Parliamentary Labour Party work would begin immediately to address concerns but warned: "We can't have the Budget defeated."
The Tories and Liberal Democrats are calling for a compensation package.
Mr Brown told Labour MPs: "I understand how difficult it is when food prices and fuel prices are rising."
"It is difficult out there and I understand that. People want to know we get it and understand their anxieties."
Ahead of local elections in England and Wales on 1 May, Mr Brown warned: "We have a responsibility to listen, to hear and to understand what is being said. But there is a responsibility on all of us to unite."
EFFECTS OF TAX CHANGES
Most people with incomes of £18,000+
Under £18,000 but aged 65+ and therefore eligible for higher personal allowances
Under £18,000 but with young children and therefore eligible for child tax credits
Under £18,000 and ineligible for working tax credits because under 25
Retired early and therefore ineligible for higher personal allowances
Part-timer working insufficient hours to qualify for tax credits
Different personal circumstances may affect final amounts
The BBC understands former deputy prime minister John Prescott spoke up to support Mr Brown and told MPs not to let "bickering" undermine "economic stability".
Some MPs said there had been a shift in feeling since a similar meeting three weeks ago. Former minister Denis MacShane told the BBC that Mr Brown's approach had been "more humane, more human and much more sympathetic".
He said he believed the problem would be sorted out before the autumn and predicted "nobody is going to start voting against the government".
Party whips have told MPs a vote against the bill will be a vote of no confidence in the government.
But Labour MP Gordon Prentice, who was also at the PLP meeting, said MPs would not be "cowed" and said he wanted the government to come up with a solution within a week.
"There is a recognition across the Parliamentary Labour Party that a terrible mistake has been made, that we are not in the business of making poor people poorer and we've got to address the issue quickly," he said.
The Finance Bill - which enacts the Budget including scrapping the 10p tax band - was given a second reading on Monday evening when MPs approved it by 298 votes to 223. The government faces a likely rebellion when the 10p rate is considered next week.
Opening the debate, Chief Secretary to the Treasury Yvette Cooper said an inquiry into child poverty would be expanded to include low earning households without children.
But she argued that the "majority of households" were better off under the package.
"It is hard in any one Budget to help everyone, and those who lose in any one year may have benefited in previous years or may also benefit in the next," she said.
The Commons Treasury committee has said single people with no children earning under £18,500 will lose up to £232 a year.
More than 70 Labour MPs have signed motions raising concerns but it is not known how many will vote against the measure next week.
Labour MP Frank Field, who has tabled an amendment calling for compensation for those who have lost out, urged the government "to bring forward specific proposals" to protect low-paid workers.
For the Conservatives, Philip Hammond said the abolition of the 10p rate had been a "sleight of hand" by former chancellor Gordon Brown - as part of his pitch for the Labour leadership.
He said Mr Brown had been trying to reach out to Middle England and had demonstrated "the cynicism that has come to personify him, as he reversed a long term political objective for short term political gain".
Low earners who would have paid income tax at the lowest, introductory 10% rate now have to pay the 20% rate. Meanwhile the basic rate of income tax has been lowered from 22p to 20p.
Ms Cooper announced the expansion of the Treasury inquiry into helping low paid families with children, to include those without.
But Liberal Democrat leader Nick Clegg said the government should be able to work out the impact on the low-paid of doubling the rate of income tax.
"This is a desperate attempt to calm Labour MPs who are taking the blame from voters for Gordon Brown's decision to hit some of the poorest workers with a big tax rise for the sake of easy headlines."
The Treasury is expected to produce proposals in time for the Pre-Budget Report this autumn, although they may not be implemented until the next budget.
Scrapping the 10p rate was part of a range of measures which came into force this month - child benefits, state pensions and tax credits have gone up. The government says the changes are already benefiting millions of people.