The men reportedly disagree over tax and spend
Tony Blair's official spokesman hailed the chancellor as one of the finest finance ministers in the world with a fine track record of achievement.
It had been suggested that tensions had built-up over Mr Brown's preference for extending tax credits set against Mr Blair believing the cash would be better spent on public services.
But the prime minister's spokesman said on Monday the two goals of social justice and improving public services were not mutually exclusive.
And he said Britain's economic health was the result of the stewardship of Mr Brown and the strength of his relationship with the prime minister - what the spokesman called one of the great strengths of the government.
Rivalry claim
The comments came as Liberal Democrat leader Charles Kennedy was expected to take advantage of the claims, telling business leaders in Cardiff that Mr Blair has ditched Britain's traditional system of cabinet government.
That follows remarks made by former Northern Ireland secretary Mo Mowlam, who told the BBC that rivalry between the prime minister and Mr Brown was "crippling" for the government.
Ms Mowlam, who stepped down from Parliament at the last election, told the BBC programme Cabinet Confidential on Saturday that the two men "aren't working together".
"When you have two people that aren't working together... it doesn't lead to positive, easy, decision making.
"You know there's a battle going on and people support, or people go to, one side or the other.
"I think that is just crippling for government."
The following day the Sunday Times reported that Mr Brown "shouted and swore" following a meeting with the prime minister.
It said a cabinet colleague described Mr Brown as being in an "evil" mood, and that he was in increasingly acrimonious battles with other ministers to maintain his position as "successor" to Mr Blair.
Tax and spend 'rifts'
The paper added that the chancellor has criticised Home Secretary David Blunkett, Health Secretary Alan Milburn, Transport Secretary Stephen Byers and Education Secretary Estelle Morris - all seen as Number Ten "favourites".
The Sunday Telegraph reported that a rift is developing between the two over tax and spending.
Home Secretary David Blunkett is one Cabinet member who has ridiculed speculation on who might succeed the prime minister.
Despite being dubbed the favourite to follow Mr Blair, Mr Blunkett insisted, on BBC One's Breakfast with Frost programme, that there was no prospect of a contest.
"Those who have good lunches and good dinners and speak on behalf of other people should reflect a little before they open their mouths.
"We are not in a contest for anything. We haven't got a vacancy.
"We have a leader who is respected from Spain to the Balkans through to the US."
There have been rumours of a feud since Mr Blair became Labour leader in 1994.
It has been widely reported that Mr Brown agreed to step aside from the leadership contest at the time, in return for Mr Blair handing power to him at some point in the future.
Both men have denied such a deal, and have gone out of their way in the past to prove they are close.