Opposition parties have called for an immediate general election as Gordon Brown does not have a "mandate to govern".
Constitutionally, Brown does not have to call an election until 2010, although he has hinted that a poll could be held as early as next year.
But as the new prime minister took up the reins of power on Wednesday, having been elected unopposed by the Labour Party, both David Cameron and Sir Menzies Campbell said he should seek an endorsement from the electorate.
The Conservative leader congratulated Brown on his WebCameron website but said that the public should have the opportunity to decide who governs.
"Of course I congratulate Gordon Brown on becoming prime minister... but there are huge problems in our country," Cameron said.
"There are problems with the NHS, as anyone can see, problems with crime in our communities, social breakdown...
"But I think with Gordon Brown [there] is someone who's been at the heart of this government for the last decade, and so he is the author of many of these problems - he can't be their solution. In a sense he can't be the change that Britain needs."
He added: "I think people should have the opportunity for change - people should be able to vote for change.
"And that's why we believe that there should be a general election straight away.
"Gordon Brown doesn't have the mandate, he wasn't elected as prime minister, and he should go to the country."
Campbell
Liberal Democrat leader Sir Menzies agreed, saying that Brown "cannot escape the last 10 years".
Labour's failures are his failures too. This is the man who has signed the cheques for the Iraq war and who raised taxes for the poorest and lowered them for the richest," he said.
"Britain needs a change in direction not just a change at the top."
He also called for an early poll, saying: "Tony Blair promised the British people that he would serve a full third term and that was the basis on which Labour were returned at the last election.
"Gordon Brown does not have a mandate to be prime minister and he should seek one by calling for a general election."
