Gordon Brown lacks a "full-throated mandate" to become prime minister and there should be an election soon after Tony Blair resigns, David Cameron says.
The Conservative leader told BBC One's Sunday AM show that Mr Blair had promised at the last general election to serve a full term.
Mr Cameron also called for a "revolution in responsibility", with less emphasis on state control.
Pensions Secretary John Hutton rejected the call for an early election.
Mr Cameron said of Mr Brown, who is widely expected to take over from Mr Blair: "I just don't really know him very well. We have only met and talked a couple of times.
"Sometimes in politics you have some friendships across the floor of the Commons but I just don't really know him.
"He's a formidable politician, no doubt about it, but I think his problem is his record."
Asked whether Mr Brown becoming prime minister would be any different to John Major's accession in 1990, Mr Cameron said: "I think there's a difference this time in that Tony Blair uniquely said before the last election that 'I'm not going to fight another election but I'm going to do a full term'.
"People elected him for a full term, so we are in a different situation."
He said: "Whoever takes over must know they haven't got that full-throated mandate from the British people, so we should have an early election."
Mr Brown's record was on of "more state control", Mr Cameron said.
The Conservatives would offer a "social responsibility revolution" with, for instance, hospitals and NHS trusts running their own affairs, rather than Whitehall.
Mr Hutton said there was no need for an election soon after Mr Blair resigns.
He told BBC One's The Politics Show: "I think we are going to implement our manifesto. That's the most important thing.
"We are going to do what we were elected to do in 2005
"Personally, I don't see the argument in favour of an election when we choose a new leader.
"I think we will continue to implement the manifesto and govern as New Labour."
But Mr Cameron said there needed to be a debate on the chancellor's record in government.
On Saturday, the chancellor accused some groups of playing "fast and loose" with the political union between England, Wales, Northern Ireland and Scotland.
But Mr Cameron said Labour was to blame for "carving up" the UK through devolution.
He also accused the government backed a version of European integration which meant "more power going from nation states".
The EU had to do more to encourage global trade, action to save the environment and help for the developing world he added.
Mr Cameron said there were "painful choices" to be made on the cost of travel, whichever party was in government.
However, if green taxes - such as those on flying - rose, others imposed on families should decline, he added.