Conservative leader David Cameron has written to Gordon Brown to ask him to "re-consider" his decision not to take part in a televised debate.
A televised debate was held in the recent French presidential elections
At a press conference on Tuesday, Mr Brown was repeatedly asked whether he would take part in a debate - in an effort to boost voters' interest.
He said there were opportunities to quiz him at prime minister's questions.
But Mr Cameron said this was not possible during election campaigns, when Parliament does not sit.
In his letter, he says: "It is true, of course, that we have the opportunity to debate matters at prime minister's questions.
"But that is a very different matter to a proper television debate during a general election campaign - when Parliament is not sitting, and when people will be most receptive to engaging in political discussion.
"I am sure, on reflection, that you will want to re-consider your position. I remain ready to hold such a debate, either between the two of us, or including the Liberal Democrat leader, whenever the opportunity arises."
Televised debates between politicians are common practice in the United States, France and elsewhere, but Tony Blair refused to take part in any during his time as prime minister.
Mr Brown said the situation in the US was different as presidents were directly elected by the people - and there was not the same opportunities for the two parties to challenge each other.
"In Britain it has got to the stage where every week there is 30 minutes devoted entirely to this.
"This allows people to ask their questions and put their views and that is exactly how it has been for many years."
He added: "The number of statements I give in the House of Commons allows all the parties to question me very regularly."
"There are plenty of opportunities for people to question me both with statements and question time in the House of Commons."
But Liberal Democrat leader Sir Menzies said: "David Cameron is a Johnny-come-lately on this issue.
"I wrote to both David Cameron and Gordon Brown challenging them to a TV debate in June this year.
"Gordon Brown's new politics is only skin deep. As the leader of his party he should take part in leaders' debates to discuss the issues facing this country. This is what people want and expect.
"I cannot wait to debate against both Gordon Brown and David Cameron."
Mr Brown, who took over as prime minister in June, has refused to rule out calling an early election - fuelling speculation he may go to the polls as early as October.