The Prime Minister has formally refused to go head-to-head with Mr Salmond, stating that the referendum is a matter for "Scots living in Scotland".
Mr Cameron said it should not become a glorified General Election and any live TV debate should instead involve Mr Salmond and Alistair Darling, the Labour MP and former Chancellor leading the pro-Union Better Together campaign, he claimed.
In a letter to the First Minister, Mr Cameron said the proposal for the TV debate was a "convenient means of deflecting attention away from the real issues - the lack of credibility of plans for a currency union, funding pens-ions and managing oil revenues".
The Prime Minister added: "You want the independence debate to be an argument between you and me; the Scottish Government and UK Government; the SNP and Conservative Party - in fact anything rather than what it really is about."
But Mr Salmond said: "The Government in which Mr Cameron serves as Prime Minister is central to the entire referendum debate from the perspective of the No campaign.
"The reality is his Government continues to make decisions affecting Scotland, such as the implementation of the hated bedroom tax and the deeply unpopular privatisation of the Royal Mail, despite the fact an overwhelming majority of Scots didn't vote for him or the Tory party.
"I have noted the Prime Minister's apparent unwillingness to take part in another General Election debate and I'm sure people will draw their own conclusions from that.
"I believe his refusal to debate Scotland's future with me can be summed up in one word - fear."