In memoirs serialised in the Sunday Times newspaper, Prescott described the tempestuous relationship between the two men in the years before Blair stood down last June, and said the prime minister had been scared to act against Brown.
Prescott's claims come at a difficult time for Brown, already struggling after crushing local election losses, collapsing opinion poll ratings and damaging revelations about his behaviour while serving in Blair's government.
In extracts from her memoirs on Saturday, Blair's wife Cherie accused Brown, who had long sought the prime minister's job, of "putting too much pressure on Tony to quit when Tony wasn't ready".
Prescott said he spent much of his time acting as a conciliator, with "hundreds" of phone calls and meetings dealing with "Blair-Brown issues".
Brown was "frustrating, annoying, bewildering and prickly", Prescott said, while Blair had reneged several times on pledges to make way for Brown as prime minister.
Prescott said he had also challenged Brown to quit as Chancellor of the Exchequer over Blair's broken promises.
"With Tony, when he was moaning on about Gordon's behaviour, I'd say 'Sack him. Find a new chancellor is that's how you really feel'. But neither would take the final step," Prescott said.
"They were caught in their own trap. Tony knew that sacking Gordon would tear the party apart."
Brown's popularity has plummeted in recent months, raising questions over whether he will face a leadership challenge ahead of national elections which must be called by 2010.
An unpopular income tax reform, rising fuel and food prices, a downturn in the housing market and criticism of Brown's leadership brought the Labour party to its worst local election performance on record earlier this month.
Since then, there has been no let-up in bad headlines for Brown.
An opinion poll in Sunday's Observer newspaper showed only one in five voters thinks Brown is doing a good job. Another poll in The Mail on Sunday showed Labour could be heading to defeat in a crucial parliamentary by-election in 10 days time.
The ICM survey carried out in the Crewe and Nantwich constituency puts the opposition Conservative Party on 43 percent, four points ahead of Labour on 39 percent, with the Liberal Democrats on 16 percent.
Last Mod: 11 Mayıs 2008, 15:38