The Prime Minister, attending a conference in central London on the family and relationships, was asked about the Scottish Government's claim that the Conservative-led UK Government was pursuing a policy of privatisation of the NHS in England, which would, because of the relationship between UK Government spending and Scottish Government spending, have a detrimental knock-on effect on health care in Scotland.
Dismissing the notion out of hand, he said: "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. So this is a desperate man, recognising the argument is going away from him, making a pretty desperate argument."
Mr Cameron 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."
With one month to go to Referendum Day, the Yes campaign has been bouyed by a rise in support in recent polls and believes, ahead of next week's second and final TV head to head between the FM and Alistair Darling, who heads the Better Together campaign, that the NHS is a policy area on which it can make a forceful argument and put the No camp on the back foot.
But pro-UK campaigners have accused Mr Salmond of scaremongering, stressing the point that, because of devolution, control of health care in Scotland has been handed wholly over to ministers in Edinburgh.