Better Together, the pro-UK campaign led by Mr Darling, reacted angrily after STV indicated it was willing to change the date at the request of the First Minister. A senior Better Together source said Mr Darling would take part on July 16, as agreed, but not at a later time to suit Mr Salmond.
Meanwhile, it emerged the BBC have intervened with proposals for a televised debate on August 12.
Last week, STV invited Mr Salmond and Mr Darling to face each other in a live debate from Edinburgh's Assembly Rooms venue on July 16. Mr Darling agreed but Mr Salmond said he would only appear on that date if he could face Prime Minister David Cameron instead.
He said he would debate with Mr Darling - if the Prime Minister continued to refuse - but only on a date after the Glasgow Commonwealth Games, which end on August 3.
A Better Together insider said: "STV told us that they would not negotiate on the date of this debate. That hard line stance lasted until Salmond decided that he didn't fancy debating Alistair. STV has simply rolled over. It is not on."
The campaign insider added: "We have accepted an invitation from the BBC for a debate on August 12."
A spokesman for the First Minister said: "This outburst at STV from the No campaign shows they are fraying at the edges. Our position is clear and has been throughout. We are grateful to the No Campaign for drawing attention to the fact the Prime Minister is feart of debating Alex Salmond."
STV was planning a debate in front of 500 people hosted by political editor, Bernard Ponsonby.
A spokeswoman for the TV channel said: "We have not received agreement from both sides on the proposed date of July 16 and are reviewing the proposed date on that basis."
A BBC spokesman confirmed its bid to stage a debate in Inverness, hosted by James Cook, on August 12.
It is understood neither leader has formally replied so far.