Mr Salmond signalled that he will pin his hopes on winning next Monday's second and final head-to-head with Alistair Darling, leader of the Better Together campaign, by focusing on the totemic issue of health care.
The TV clash - to be broadcast across the whole of the UK - could be even more crucial than the first, which most commen-tators gave to Mr Darling, because the following day around 680,000 postal votes, 17 per cent of the total 4.1m eligible ballots, will be issued and, customarily, half will be cast within 48 hours.
In Arbroath, where the historic declaration was made in 1320, setting out Scotland's case as an independent, sovereign kingdom, the First Minister published the Scottish Government's Declara-tion of Opportunity, saying independence would provide Scots with the chance of protecting the NHS.
"In Scotland, because we control health policy, we have been able to resist the West-minster privatisation drive; but we don't control Scotland's budget. So when the Tory-led Westminster Government privatises services and cuts state provision, those cuts are passed directly on to Scotland."
He added: "So the only guarantee, the only certain way of protecting our precious, publicly-funded NHS, is independence."
But after making a speech in London promoting the family, the Prime Minister brushed aside Mr Salmond's warning, saying it was baseless.
"Health is a devolved issue, so the only person who could, if they wanted to, introduce more private provision into the NHS in Scotland is Alex Salmond," declared Mr Cameron. "So this is a desperate man, recognising the argument is going away from him, making a pretty desperate argument."
The Prime Minister added: "Because of the protection on NHS spending that the UK Government has given - that we would not cut NHS spending while we have had to make difficult decisions elsewhere - that has made sure under the Barnett Formula that money is available for Scotland as well, so that argument does not stack up at all."
Elsewhere, Douglas Alexander, for Labour, also seized on Mr Salmond's acceptance that, because of increased NHS spending in England, there were positive spending consequentials for the health service in Scotland.
The Shadow Foreign Secretary stressed how the Mr Salmond had "destroyed his own argument on NHS funding by admitting that more money is coming to Scotland to spend on the NHS through the Barnett Formula". The Paisley MP added: "Everyone can now see his NHS scare stories for what they are."
But Blair Jenkins, head of Yes Scotland, claimed Scots were "waking up to the extent to which the NHS in England is being privatised" and the arguments for independence to prevent this were "touching a real emotional nerve with people, particularly women".
Later as Mr Salmond toured Arbroath, he claimed the NHS was "the biggest issue in this campaign at the present moment and it is the one that's moving minds and moving votes".
Denying the claim of scare-mongering, the SNP leader said: "It is an entirely legitimate point to say that charging regimes, fragmentation, privatisation in England causes a reduction in the health budget."
Turning to Monday's TV debate, the First Minister said the NHS would be "examined a great deal", adding: "It was a misfor-tune that the first television debate didn't focus more on the health service but I am sure the second debate will provide ample opportunity to develop these arguments."
Meantime, Chuka Umunna, the Shadow Business Secretary, who will be in Scotland today on the referendum campaign trail, called for Mr Darling to return to frontline Westminster politics after the independence vote.
He said the former Chancellor had a "big contribution to make" and was one of the "biggest beasts" of the Labour Party.
Mr Darling has made clear he will only think about his future plans after September 18.
l The NHS will recruit 500 apprentices over the next three years, Health Secretary Alex Neil announced.
The apprentices will initially be recruited to the adminis-tration, IT and facilities manage-ment sectors.
Mr Neil announced the modern apprenticeships during a visit to Dundee's Ninewells Hospital, where he said: "Our commitment to 500 new modern apprentices represents an investment in our young people and the future of NHS Scotland.
"Recruiting modern appren-tices not only provides real opportunities for our young people, it also helps to ensure that NHS Scotland has a workforce with the skills and expertise."