Chancellor Gordon Brown is said to have told union chiefs he would refuse to reverse Tony Blair's NHS reforms.
Gordon Brown is not allaying union concerns on the NHS
Mr Brown was addressing a private dinner at the TUC conference in Brighton, after Mr Blair had delivered his platform speech to union delegates.
Mr Brown's aides say he supported the current reform agenda in his speech.
Transport union boss Tony Woodley praised Mr Brown's "unifying" message, but the GMB's Paul Kenny said fears remained on privatisation of services.
'Renewing the NHS'
The prime minister and chancellor take it in turns each year to give the TUC platform address and union leaders' private dinner speech.
Mr Brown's team portrayed his speech as a show of unity with the prime minister, who faced a walkout from about 20 rail union delegates over his stance on "privatising public services".
Members of public service union Unison have also decided to stage the first national strike in the NHS for nearly 20 years in protest at the service's supply arm being sold off.
And the TUC conference has voiced anger at the use of private firms to run hospitals and treatment centres.
Ahead of the speech, aides said Mr Brown would say: "I urge all to support Tony Blair in what he said about our reforms in health so that we can show that a universal health service free to all at the point of need is renewed and reinvigorated through reform to serve the British people.
"For the British people the best insurance policy in the world, but also a beacon of hope to the rest of the world, that the way forward for the future of developing countries will also be universal health care like ours."
Some at the dinner cast doubt on the idea that Mr Brown had backed the reforms in such forthright terms in what was an unscripted speech.
But they said he had praised Mr Blair for an "excellent speech".
The chancellor's aides say he made clear that investment had to be coupled with reform to keep a health service free to all at the point of need.
They said he also said he had made clear he was fully committed to the goal of full employment.
Mr Brown said the labour movement's mission was still the abolition of poverty.
'Manufacturing has a future'
Mr Brown is also said to have echoed Mr Blair's appeal for Britons to be "strong, not scared" in the face of the challenge of globalisation.
He was said to have argued that British manufacturing could have a strong future if there was investment in the skills needed to compete in a global market place.
Mr Woodley, leader of the Transport and General Workers Union, said he was stunned.
"I have just seen a speech that I have not seen equalled from a trade union leader in our country for a number of years, a guy who has put out a vision on his ideas for our country," he told BBC News.
"But at the same time it was a unifying and uniting speech, making plain the difference between a Labour government and a David Cameron Conservative government."
But Mr Woodley said he was not ready to endorse Mr Brown's leadership ambitions.
"What we need is substance now on top of that speech," he said.
For some union leaders, it appears to have been the difference in Mr Brown's tone to Mr Blair's speech that they found persuasive.
One said: "It's amazing how you can say the same things and have a completely different effect."
But Mark Serwotka, from the Public and Commercial Services union, said: "What was significant and disappointing to me was that whilst he talked about big picture international issues, he didn't deal with any of the issues that had dominated this conference."
And Mr Kenny, general secretary of the GMB union, said Mr Brown had appeared very relaxed and delivered a confident and polished performance.
"However, in content terms there remains the thorny issue of privatisation and we are miles apart on that issue," said Mr Kenny.
The speeches come after Northern Ireland Secretary Peter Hain said he would stand in the race to become Labour's deputy leader.
Mr Hain, who says Mr Brown should be the next prime minister, says Labour needs to reconnect with its grass roots.