The position was stated as Mr Cameron admitted that as an English "Tory toff" his appeal in the referendum campaign did not stretch across all parts of Scotland.
During Prime Minister's Questions, Mr Cameron said the SNP was experiencing "mounting frustration" because it knew it was losing the argument in the independence debate.
At the weekend Mr Salmond again demanded the PM, as head of the UK Government, debate him face to face on the independence issue but, as before, Mr Cameron refused, leading the First Minister to accuse him of a "mix of arrogance and fear".
During PMQs, Angus Robertson, the Nationalist leader at Westminster, sought to put Mr Cameron on the spot, referring to how a pro-UK "stick with us" campaign - revealed in The Herald on Monday - was to be launched south of the border, involving as yet unnamed celebrities.
The Moray MP said: "The Prime Minister's anti-independence campaign launched an initiative this week encouraging people outside Scotland to take part in the debate. Given that, why won't he debate First Minister Alex Salmond on television?"
Mr Cameron said the continuing calls for a PM/FM debate displayed a "mounting frustration amongst those calling for Scotland's separation from the rest of the United Kingdom because they know they are losing the argument".
He went on: "They know they are losing the argument about jobs, they know they are losing the argument about investment, they completely lost the argument about the future of the pound sterling. They are losing the argument about Europe.
"Yes, of course there should be a debate, but it is a debate between people in Scotland. The leader of the In campaign should debate with the leader of the Out campaign."
Mr Cameron then told Mr Robertson: "Of course, you, as the lackey of Alex Salmond, want to change the terms of the debate but I am not falling for that one."
In later exchanges, Labour's Ian Davidson told the PM: "Without seeking to give offence to you, can I tell you that the last person Scots, who support the No campaign, want to have as their representative is a Tory toff from the home counties, even one with a fine haircut?"
This was a reference to Lino Carbosiero, Mr Cameron's hairdresser, who controversially received an MBE in the New Year's Honours list.
The Conservative leader replied: "I humbly accept that while I am sure there are many people in Scotland who would like to hear me talk about this issue, my appeal doesn't stretch to every single part."
But he again stressed the Nationalists knew they were losing the argument, so wanted to change the question. "It's the oldest trick in the book and we can all see it coming," added Mr Cameron.
Outside the chamber, asked if the PM would refuse Mr Salmond's challenge no matter how many times he made it, his spokesman replied: "That's correct."
Earlier this week, an SNP-commissioned poll showed 63% of Scots and 56% of voters in the rest of the UK thought Mr Cameron should accept the challenge to debate with Mr Salmond.
Last night, Mr Robertson said: "David Cameron's position is increasingly incoherent. It is his anti-independence campaign and he is now asking people outside Scotland to get involved, yet he still refuses point blank to debate himself.
"It is time for him to put up or shut up."