Ed Miliband has been challenged by David Cameron to state that Labour will not do a post-election deal with the SNP amid warnings a pact could trigger a constitutional crisis.
The Labour leader used a speech in Scotland to warn that a vote for the SNP would make it more likely that the country would face another five years of Tory rule and Opposition sources dismissed Mr Cameron's demand as "ludicrous".
The Prime Minister said Mr Miliband should explicitly rule out a deal with the SNP "if he cares about this country".
Mr Cameron's remarks, at a campaign event in Harrow, north London, followed a suggestion by former Tory chairman Lord Baker that a grand coalition between the Conservatives and Labour may be necessary to avoid the SNP holding the balance of power at Westminster.
Nicola Sturgeon's party has benefited from a poll surge in recent months which could see them make massive gains in Scotland, potentially casting her as kingmaker following May 7's election.
The SNP leader has ruled out supporting a Tory government and said it was "unlikely" the SNP would enter a formal coalition with Labour in the event of a hung parliament, but indicated her MPs could work with Mr Miliband's party on an "issue-by-issue basis".
The Prime Minister said a Labour administration supported by the SNP's votes would be the "worst outcome" for the UK.
He said: "You could end up with an alliance between the people who want to bankrupt Britain and the people who want to break up Britain.
"Even today, Ed Miliband will not rule out a deal or backing from the SNP.
"If he cares about this country, he should do so. You cannot let the people who want to break up our country into the government of our country."
In a speech to the Scottish Labour conference in Edinburgh Mr Miliband sought to persuade would-be SNP voters that they could end up returning Mr Cameron to Number 10.
He said: "Every vote cast for another party, including the SNP, makes that prospect of a Tory government more likely.
"It is just a matter of arithmetic.
"Because every one less Labour MP makes it more likely the Tories will be the largest party."
The Labour leader, who is also said to be under pressure from Scottish MPs to rule out a deal with the SNP, made no mention of the possibility of a pact in his keynote speech.
But a senior Labour source dismissed Mr Cameron's call as "Tory gamesmanship" at a time when the Prime Minister is under pressure over his refusal to take part in the TV debates proposed by broadcasters ahead of the election.
The source said: "If David Cameron is going to play these games, he is going to have to answer whether he will do a deal with Ukip.
"The SNP don't want a coalition and we are not seeking one."
The prospect of an increased SNP presence in the Commons led Lord Baker to suggest that a coalition between the two largest parties may be the only way to avoid a constitutional crisis.
Writing in The Independent, he said: " What is at risk is the continuing unity of the United Kingdom. In order to preserve that unity another way should be found.
"This could be a joint government of the Labour and Conservative parties: quite unthinkable at the moment, and at this time likely to be rejected by both of them - but this is what has happened in Germany."
He suggested that a joint administration could be established for two years, with its main purpose being to establish a constitutional convention aimed at "preserving the United Kingdom and ensuring that devolution, which is the order of the day, is achieved in an orderly, fair, consistent and coherent way".
Scottish Labour leader Jim Murphy dismissed the idea of a grand coalition as "ludicrous" and added: " I don't need lessons from Tory dinosaurs about how to run Scotland."
He told the BBC: "What a ludicrous, ludicrous idea. That's never going to happen."
Leading entrepreneur Lord Bilimoria, an independent crossbench peer, warned that it would be a "disaster" for the economy if Mr Miliband won power with the help of the SNP.
The Cobra Beer boss said the prospect of a deal between Labour and the SNP was "terrifying".
"I am very worried about Ed Miliband and Labour being in government this time," he told The Telegraph.
"I find the prospect of a Labour-SNP coalition quite frankly terrifying, on a number of counts.
"I am seriously concerned about Ed Miliband's lack of experience and understanding and his priorities. I am not alone. Every single entrepreneur I have spoken to believes exactly what I am saying."
Lord Bilimoria hit out at Labour's plans for a mansion tax on homes worth more than £2 million and proposals to restore the 50p income tax band.
The peer also warned that the SNP cannot be trusted with the economy and are a "high public spending party".
He said: "If you combine that with Labour also wanting to spend more and put up taxes, and therefore jeopardise wealth creation and job creation, then it is a recipe for disaster.
"Ed Miliband still has the opportunity to demonstrate that he understands business and will be pro-growth, pro-employment and pro-wealth creation. He has to demonstrate that."
He said he was also concerned about the prospect of the SNP and Labour deciding to scrap the Trident nuclear weapon system.
"To get rid of Trident would be the number one irresponsible thing that any government could do," he said. "That is the most terrifying aspect."