Conservative leader Michael Howard has urged Tony Blair to "bring it on" and take part in a live election debate.
Michael Howard wants a UK version of the US presidential debates
He said the Prime Minister would be "running scared" if he refused his calls for the country's first, US-style televised head-to-head.
Before the 2001 election, plans for a debate between Mr Blair, William Hague and Charles Kennedy collapsed.
In 1997 a debate between Mr Blair and John Major was also cancelled when a format could not be agreed.
'Let the people decide'
There have been three televised live debates in the United States between George W Bush and rival John Kerry.
Mr Howard believes such a contest in this country before the next general election would "re-engage the electorate".
Speaking to the Sunday Telegraph, Mr Howard urged Mr Blair to "bring it on - and let the people decide".
Michael Howard says a debate would make politicians more accountable
He said: "All of us in politics should be worried about falling turnout at elections.
"Labour claims that it wants to do something about it, but its answer is all-postal ballots, which have shown themselves open to fraud and corruption."
The Tory leader said: "Our answer is much more effective - let politicians be accountable. What better way could there be than for the Prime Minister to debate with me before the next election?
"Debates could be part of the process of re-engaging the electorate and making politicians more accountable.
"That is why I am so keen to debate with Tony Blair. And, if he refuses, the electorate will be entitled to ask, `What is he afraid of?"'.
On the eve of the 2001 election Mr Blair was accused of being "chicken" when he turned down the opportunity to take part in a planned debate between Britain's three main political parties.
Previous plans for debates with the Prime Minister have collapsed
But the then Leader of the Commons, Margaret Beckett, defended Mr Blair's decision, saying TV debates were "geared to an American-style election" and would focus attention on the individuals rather than the political parties.
Under the proposals, Mr Blair would have faced the then Tory leader William Hague and Liberal Democrat leader Charles Kennedy in two live debates screened
separately on BBC1 and ITV.
Each would have covered three key subjects, with each man making brief opening and closing statements and then cross-examining each other
over their answers.
Television bosses have continually appealed for such debates, arguing that they would boost public interest in the election process.
It is thought unlikely Mr Blair will be goaded into agreeing to his rival's challenge, as many believe he would stand to lose more than he would gain.