"The government is collapsing before our eyes," said Cameron, tipped by opinion polls to be elected as premier within a year.
"Why doesn't he take the one act of authority left to him: get down to the palace, ask for a dissolution (of parliament), call that election?"
Nick Clegg, leader of the second opposition Liberal Democrats, said Brown's Labour Party was "in total meltdown."
The premier hit back by stressing his policies on pulling Britain out of recession and dismissing the Conservatives as nothing but "talk, talk and talk," prompting Cameron to charge that he was "in denial."
The exchanges came on the eve of Thursday's European Parliament and English local council elections, which are predicted to be a bloodbath for Labour.
A new YouGov poll for the Daily Telegraph among people certain to vote in the European elections suggested Labour can count on just 16 percent support.
That puts them in third place behind the Conservatives and, damagingly, behind the anti-EU party, the UK Independence Party (Ukip), which is on 18 percent.
Earlier, Communities and Local Government Secretary Hazel Blears became the fourth minister in two days to announce she was quitting.
She said she wanted to return to "grassroots" politics but had faced recent criticism from Brown over her expense claims.
Home Secretary Jacqui Smith, left embarrassed after it emerged she claimed on expenses for two adult films watched by her husband, meanwhile confirmed she will step down at the next cabinet reshuffle, expected as early as Friday.
On Tuesday, children's minister Beverley Hughes said she was going and will reportedly be joined by Cabinet Office minister Tom Watson, a close Brown ally.
The recent row over lavish expense claims by lawmakers, which has led 15 members of parliament to say they will quit, has piled fresh pressure on Brown's already unpopular premiership amid accusations he has been slow to respond to public anger.
Some reports suggest he could face a leadership challenge before the next general election, which must be held within a year, possibly from Health Secretary Alan Johnson.
Sky News television reported that an email was circulating late Wednesday among Labour MPs encouraging Brown to step down, while the BBC said it had seen a letter from a Labour MP, likely be circulated on Friday, urging him to quit.
Labour Party rules state that 72 MPs must sign a motion of no-confidence to trigger a leadership election. Labour currently has 350 MPs, a majority of 63.
Johnson expressed support for Brown Wednesday, and some commentators say there is little interest from anyone in taking over the helm of a party which looks likely to be forced out of office by the Conservatives within months.
An Ipsos Mori poll Tuesday said support for Labour had plunged to 18 percent, with the Conservatives on 40 points.
"Rats Desert Sinking Ship" and "Meltbrown" were among headlines Wednesday, while The Guardian newspaper, traditionally sympathetic to Brown and Labour, symbolically withdrew its support for him.
"It is time to cut him loose," it said in an extended editorial.
Labour "faces its worst defeat in its history tomorrow but the prime minister does not recognise his direct responsibility for the mayhem.
"The truth is that there is no vision from him, no plan, no argument for the future and no support."
There are widespread reports that finance minister Alistair Darling, who has led Britain's response to the recession, could also be demoted in a reshuffle.
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