In an unusual alliance, the Labour, Liberal Democrat and Ukip leaders have sent identical letters to the Prime Minister warning that it would be "unacceptable" for him to block the debates.
They are demanding Mr Cameron be "empty chaired" by broadcasters if he does not join give ground ahead of the 7 May 2015 election.
Mr Cameron has already stipulated he would not participate unless the Green Party was included alongside Ukip in the encounters.
The letters claimed the debates were watched by more than 20 million people during the 2010 election campaigns and "enthusiastically endorsed by all those who took part, including yourself".
The letter reads: "In recent days, you have announced that you are unwilling to take part in debates as proposed by the main broadcasters for the 2015 General Election,” the missives added.
"I believe it would be a major setback to our democratic processes if these debates were not repeated in 2015 because of one politician's unwillingness to participate.
"I hope you will agree that the decision as to who should take part in the televised debates should not be in the hands of any party leader, each of whom inevitably has their own political interests to defend. It must be a decision independently and objectively arrived at."
The leaders insisted the broadcasters were under strict obligations of political impartiality and had made an "objective determination" about who should participate.
"While each of the other parties invited to take part in the debates has their own views on the proposal and the levels of participation offered and will continue to make their case in this regard, we all accept the independence and impartiality of the broadcasters and have committed to take part in the debates," the letters added.
"It would be unacceptable if the political self-interest of one party leader were to deny the public the opportunity to see their leaders debate in public.
"Therefore, if you are unwilling to reconsider, the three party leaders who have committed to participate will ask the broadcasters to press ahead with the debates and provide an empty podium should you have a last minute change of heart.
"These debates are not the property of the politicians and I do not believe the public will accept lightly the prospect of any politician seeking to block them."
Additional reporting by PAReuse content