The call came as the Prime Minister hit out at Mr Salmond, with the row between the men becoming increasingly rancorous.
Mr Cameron wrote to Mr Salmond last week refusing to take part in a head to head televised debate before next year's referendum.
The SNP insist the Prime Minister cannot opt out of a debate his government is so heavily involved with.
But Downing Street say it is right that independence is debated and decided among Scots and that the First Minister should take on No campaign leader Alistair Darling.
No. 10 sources yesterday indicated the Prime Minister did not intend to "blink" on the issue.
Earlier the Conservative leader said: "Alex Salmond wants the (referendum) question to be about anything other than the question. He would like to debate the SNP versus the Tory party or Scotland versus England. It's not. It's a debate between Scots about their future. What it should be is Alistair Darling, leader of the No campaign, and Alex Salmond, leader of the Yes Campaign."
In a letter sent to Downing Street, the First Minister has set out what he said were the six reasons why they have to have a head-to-head.
He wrote to Mr Cameron: "Either you stand up and debate or butt out of the debate for good.
"The case for a head-to-head debate between us is unanswerable. You should reconsider."
Mr Salmond also accused Mr Cameron of seeking "power without responsibility" telling him his government was "central" to the entire referendum debate.
He called on Mr Cameron to appear to "spell out your Government's plans to cut public spending in Scotland" and explain what extra powers Scots could gain in the event of No vote.
Mr Salmond said there were questions Mr Darling cannot answer, including why the UK Government will not negotiate issues such as currency or defence prior to next year's vote.
He said: "Many Tory MPs wish Scotland's funding to be slashed above and beyond the huge austerity squeeze already taking place. This is deeply concerning and I believe that a debate on such a crucial issue should take place so you can spell out your Government's plans to cut public spending in Scotland in the event there is a No vote."