Mr Brown said he wanted to focus on the "difficult" economy
The prime minister has dismissed claims that Tony Blair believes he cannot beat David Cameron in an election.
Former Labour fundraiser Lord Levy said on Sunday that Mr Blair believed Gordon Brown could not beat the Tory leader.
But Mr Brown said: "The issues ahead of us are more important than a few comments from one or two people." Mr Blair's office has denied the claims.
Mr Brown's comments come as the parties enter the final days of campaigning for Thursday's local and mayoral elections.
He told the BBC steering the economy through difficult times was more important than "gossip or rumour".
10p tax row
Conservative leader David Cameron will later promise to abolish poverty altogether as he stakes his claim to natural Labour territory.
The Tory leader will accuse Gordon Brown of making child poverty worse and urge him to publish the latest figures before Thursday's polls.
The Lib Dems are also gearing up for the elections in England and Wales at which they are defending 750 seats.
But deputy leader Vince Cable admitted on Sunday that the party was "not doing as well as we hoped we would be" in the opinion polls.
The Lib Dems and Tories both hope voters will punish Labour over the abolition of the 10p rate, as the issue comes before the Commons again later.
They claim most of those affected by the change would still be worse off even after last week's concessions - and some of Mr Brown's own MPs believe the row is hurting the party on the doorstep.
Graham Stringer, Labour MP for Manchester Blackley, said he still needed reassurances from the government about whether individuals would "get their money back or not".
"The announcements have been ambiguous to say the least as to whether people will be compensated, when they will be compensated," he said.
In an interview with BBC local radio stations, Mr Brown admitted that abolishing the 10p rate was an "omission" but he believed he still had the support of the British people.
Asked later if he was sorry over the whole 10p tax rate situation, Mr Brown said: "Well of course because it's unfortunate when things go wrong for people and we have tried to sort that out immediately, in the last few days."
But he also insisted that more people were left better-off by the tax changes in the 2007 budget, which he said had helped pensioners and families with children.
Mr Brown has also dismissed Lord Levy's comments, adding that his predecessor's office "has made it clear that this is not an accurate reflection of what Mr Blair has said".
"I'm going to concentrate on the job ahead, on the priorities that matter for the British people and not on gossip or rumour, or statements made by one or two people," the prime minister said.
He insisted that his priorities were "steering the economy through very difficult circumstances" and safeguarding the livelihoods of Britain's families.
Mr Brown acknowledged that he was forced to reassess last year's budget, which was his final one as chancellor, after the furious reaction to the scrapping of the 10p tax rate.
"Now we have dealt with that with the proposals we put forward last week," he said.
"But I think the background to the budget that people will probably remember most years from now is that we've reduced the basic rate of income tax from 22p to 20p, and we've done a lot more to help family poverty be eased."
He added that the strike by teachers over pay may have been controversial, but the profession's three-year wage deal was necessary to secure economic stability.
Mr Brown also said that he hoped that the dispute between management and workers at the Grangemouth refinery - which has led to fears of panic-buying and fuel shortages - could be settled by arbitration.
Lord Levy's comments came in an interview with the Mail on Sunday, timed to coincide with the serialisation of his memoirs.
The former fundraiser and Middle East envoy criticised the "lack of strong leadership" in the Labour Party.
He also claimed Mr Blair had told him Gordon Brown could not beat Tory leader David Cameron in an election.
The newspaper quotes the peer as saying Mr Blair claimed he was convinced he could win a fourth term if he stayed on at Number 10.
"But Gordon? 'He can't defeat Cameron,' Tony told me," Lord Levy writes.
"Blair believed Cameron had major strengths - political timing, a winning personality and a natural ability to communicate to Middle England that Gordon would be unable ever to match."
The comments were strongly denied by a spokesman for Tony Blair who said they did not reflect the former PM's views.