Although the First Minister last night continued to urge Cameron to debate with him, he indicated that if the Prime Minister refused, he would be prepared to accept Darling or another No campaign nominee as a substitute.
The change of tack comes after more than a year of Salmond insisting that his first TV debate of the independence referendum had to be with Cameron, and the Prime Minister refusing to accept.
Deputy First Minister Nicola Sturgeon told the Sunday Herald yesterday it was now "'game on' in the contest over Scotland's future". She said: "David Cameron should accept the offer of a head-to-head debate with the First Minister, which is the one that all of Scotland wants to see.
"Should the Prime Minister continue to duck this debate, the First Minister is willing to take on Alistair Darling as the Tories' nominated substitute.
"But David Cameron should know that once that contest has happened and the First Minister has effectively removed Mr Darling as his human shield, we will be knocking on Downing Street's door urging him to face up to his democratic responsibilities and finally accept a head-to-head debate.
"It's now 'game on' in the contest over Scotland's future - we will soon have a major head-to-head referendum debate live on prime-time TV."
The shift was also confirmed in a letter from the First Minister's office to Gordon Macmillan, head of news at STV, who had invited Salmond take part in a live debate on July 16.
Geoff Aberdein, the First Minister's chief of staff, wrote: "Should the Prime Minister continue to refuse to participate in a head-to-head televised debate, the First Minister will indeed agree in principle to debate with Alistair Darling or another No Campaign nominee … on a date shortly after the Commonwealth Games." The Games end on August 3.
Darling, chairman of the Better Together campaign, has long said Salmond should debate with him, not Cameron, arguing that the Prime Minister does not have a vote in the referendum, and that the debate is one between Scots, not Edinburgh versus London or the SNP versus the Tories.
However, Salmond is still likely to face criticism. His opponents will claim that by blinking first he has shown himself to be a bluffer, and so may be bluffing about far more in the campaign, whereas Cameron has stood firm, and so can be trusted when he rules out a currency union and promises more powers in the event of a No vote.
Unionists are also likely to portray Salmond's agreement as a climbdown and a sign of anxiety within the Yes campaign that it remains behind in the polls with only three months until the ballot on September 18.
The traditional political wisdom is that the losing side is always the most enthusiastic for a debate because it has to make up ground.
SNP insiders insist Salmond's preference remains a head-to-head debate with Cameron, and argue that the voters deserve to hear the arguments even if Cameron is unwilling to do the right thing. Earlier this year, a poll found the majority of Scottish voters and the majority of Conservative, Labour and Liberal Democrat supporters in the rest of the UK wanted Cameron to meet Salmond in a TV debate.
In a letter to Cameron yesterday, Salmond gave no hint that he would accept a substitute and said the case for Cameron's involvement in the STV debate was "overwhelming", especially given the Tory offer of more devolution in the event of a No vote.
Salmond wrote: "The fundamental argument at the heart of the case for independence is that decisions affecting Scotland should be taken by those who choose to work and live here. Your argument is that many should be taken at Westminster.
"Crucially, the Conservatives now claim to be committed to delivering more powers to Scotland in the event of a No vote. However, that is something which could only be done via Westminster and is entirely dependent on the proposals you would intend to place in your election manifesto. As such, the people of Scotland deserve to know exactly what your alternative constitutional position to independence is before the referendum takes place, and a live debate is the perfect formula for such alternative visions to be aired."
After the SNP's majority win in 2011's Holyrood elections, Cameron said that if there was an independence referendum he would "campaign to keep our United Kingdom together with every single fibre that I have". But although he signed the Edinburgh Agreement 18 months later enabling the referendum to go ahead, his contributions since have been limited.
Last September, he formally confirmed he would not debate with Salmond, and said the First Minister should face Darling instead. Cameron said it was reasonable "to pick your own team's captain, but not your opponent's as well", while Salmond called Cameron "feart".
The First Minister returned to the subject in the New Year, attributing Cameron's reluctance to "partly arrogance and partly fear". Cameron said Salmond wanted to argue over a debate because he was losing the more substantial arguments over independence.
Earlier this month, former Labour prime minister Gordon Brown said it would be a "good idea" if Cameron could debate with Salmond, comments which resulted in further demands from the SNP for a showdown.
The STV plan is for a live two-hour debate in front of a 500-strong audience of Yes, No and undecided voters. The campaign representatives would be quizzed by STV political editor Bernard Ponsonby, then the two speakers would cross-examine each other, and members of the audience would put questions.