The call for the debate came afte research by Leeds University found debates increased viewers’ interest in politics by 30%.
Jeremy Corbyn has challenged David Cameron to take part in an annual “state of the nation” televised debate with other political leaders to help the public engage more in politics.
The Labour leader urged his rival not to “shrink” from a general election-style public contest. Scottish National party leader Nicola Sturgeon and the Liberal Democrat leader, Tim Farron, would sign up if the prime minister accepted the challenge, the Independent was told.
“People are entitled to know more about their political leaders and to have their government held to account by the elected opposition in every way possible,” he told the newspaper.
“It is crucial that the prime minister and government are held to account, both inside and outside parliament, throughout their period in office – not just at election time.”
A senior Conservative source dismissed Corbyn’s challenge as a “desperate attempt by Labour to distract voters from the deep divisions that have left the party in turmoil”.
TV debates were first held at the 2010 election, when Cameron took on then prime minister Gordon Brown and Lib Dem leader Nick Clegg in three debates, which helped propel Clegg to public prominence.
Cameron’s reservations resulted in tortured negotiations before the 2015 election, which produced a head-to-head debate with Labour leader Ed Miliband; a seven-way clash involving the Lib Dems, the Green party, Ukip, the SNP and Plaid Cymru and one between opposition leaders.
It is thought any annual debate would have to adopt the wider format including all major parties.
The call for a debate came after research by the University of Leeds found the debates increased viewers’ interest in politics by 30%.
Corbyn, who has made greater public engagement a theme of his leadership, said: “Democracy relies on the participation of the people. No political leader should shrink from the chance to engage more fully with the public and to test their arguments in debate. It is clear that televised debates can engage more people in politics, so we should seize the opportunity to hold them more regularly.”
Farron accused Cameron of being “two-faced” about the issue for years. “He should, for once in his life, match his words with deeds,” he said. I will lay out why the Liberal Democrats are the only real alternative to the Conservatives – both socially just and fiscally responsible.”
A spokeswoman for the SNP said: “The televised debates earlier this year brought the election campaign alive and were far, far better for having a full range of participants – unlike in 2010 – which properly reflected the diverse range of political choices.”
Sturgeon’s performances in the election debates were very popular with voters.
A No 10 source said: “We haven’t been approached about this proposal and would need to see more details. But the PM is happy to be held to account every week at prime minister’s questions by MPs.”