The SNP are "perpetrating a lie" about protecting the NHS with independence, Gordon Brown has said.
The former prime minister said Holyrood already has the power to keep the health service in public hands.
He said the SNP should make way for a Labour government in Scotland if they continued to say they were "powerless".
Health Secretary Alex Neil criticised Mr Brown's remarks and said the NHS would be best protected once Scotland had full control of its finances.
Mr Brown was speaking at a campaign event in Clydebank, West Dunbartonshire.
During the event, he sought to attack the SNP's argument on health services.
He also welcomed a vow by the three Westminster leaders to enhance Holyrood's powers in the event of a "No" vote.
What might independence mean for Scotland's NHS?
The Scottish Parliament fully runs the NHS in Scotland. Campaigners for independence say a "Yes" vote would not change the day-to-day workings of the health service, but would provide new opportunities to tackle health inequalities.
Those arguing to keep Scotland in the Union believe the health service is better secured for the future as part of the UK.
BBC Scotland's health correspondent Eleanor Bradford looks more in-depth at the issue of health and the referendum debate.
David Cameron, Ed Miliband and Nick Clegg made the pledge in a signed letter which appears on the front page of the Daily Record newspaper.
Mr Brown said: "I think people are going to come to the conclusion that the change they really want is to have a Scottish Parliament as part of the UK, not the change that the SNP want, which is the chaos of a separate state."
"The NHS lie of the Scottish National Party has been exposed.
"The Scottish Parliament can keep the NHS in public hands with its existing powers."
He added: "If the SNP continue to say they are powerless to protect the NHS in Scotland, let them make way for a Labour government in Scotland and we will protect the NHS."
Mr Brown said Labour would never allow the health service to be privatised in Scotland.
Welcoming the pledge from the three Westminster leaders, he said Scottish people, with the powers already available to Holyrood, could protect the NHS.
Mr Neil, however, said Mr Brown's comments were a "spectacular own goal".
He said: "We believe it would be far better to protect Scotland's budget before the Tories get the chance to cut it in the first place.
"The main budget challenge identified in the NHS budget planning paper is as a direct result of Westminster decision-making on pensions.
"Only with a Yes vote and full control of Scotland's finances will we be able to properly protect Scotland's NHS."
Mr Brown's words came as confidential papers passed to the BBC suggested a radical cost-saving plan is to implemented in NHS Scotland after the referendum.
Papers presented to a meeting of health board chief executives and civil servants last month suggest the NHS is facing a £400m funding gap, and sweeping changes need to be made for boards to break even.
A whistleblower told the BBC "services are unsustainable right across Scotland".
However, the Scottish government said the paper was "part of the regular discussions among NHS leaders to plan for NHS Scotland's future".