No 10 insists Andrew Lansley has David Cameron's "full support", despite a Downing Street source reportedly saying the health secretary "should be taken out and shot".
Mr Lansley is coming under criticism for his planned NHS changes, including giving GPs more control over budgets.
But the prime minister's spokeswoman said the government was "very clear" in its support of the health secretary.
However, Labour accused Mr Cameron of trying to "scapegoat" Mr Lansley.
Changes to the NHS in England, contained in the Health and Social Care Bill, will be debated by peers on Wednesday.
Under the plans, groups of GPs will take charge of much of the NHS budget from managers working for primary care trusts, while more competition with the private sector will be encouraged.
But several health bodies, including the British Medical Association and the Royal College of Nursing, have voiced concerns. The Royal College of GPs wrote last week to Mr Cameron to ask for the bill - which is also opposed by Labour - to be scrapped.
The Times newspaper quotes an unnamed "Downing Street source" as saying that Mr Lansley "should be taken out and shot".
It also claims there have been discussions within No 10 about ennobling former Labour Health Secretary Alan Milburn to allow him to replace Mr Lansley.
But a Downing Street spokeswoman said: "The prime minister backs Andrew Lansley and he backs the reforms we are pushing through Parliament in order to deliver a better health service for the future."
She added that she "did not recognise" reports of Mr Milburn's name being floated as a possible replacement.
The spokeswoman also said: "As far as we are concerned, the reforms are going to deliver a better NHS, one which will be freer of bureaucracy and have less political interference. It will mean that health care workers can get on with delivering care to patients.
"We have made our position very clear about what the reforms we are legislating for will do to improve the NHS and put the powers and decision-making ability into GPs' hands."
Asked whether the prime minister was concerned about the scale of opposition, his spokeswoman said: "Understandably, lots of people have different views on our reforms, we accept that.
"We are very clear that they will deliver an NHS which is freer of bureaucracy. The fact is that we have to reform the NHS."
For Labour, shadow health secretary Andy Burnham said: "David Cameron must make an urgent statement and clarify whether these remarks come from a rogue source, or reflect his own and majority opinion in 10 Downing Street.
"A campaign is clearly under way to scapegoat Andrew Lansley. But it is David Cameron who has put the NHS on a knife edge and it can't afford to have a lame-duck secretary of state in charge who does not have authority and the personal support of the prime minister.
"Rather than looking for someone else to blame, he must now take responsibility for breaking his personal promises to NHS staff."