Mr Lansley clashed publicly with a vocal opponent of his health service reforms yesterday as he entered Downing Street for a summit to discuss the controversial changes.
The Prime Minister backed his colleague today, despite an opinion poll showing a majority of voters were in favour of ditching the legislation altogether.
Asked if he would sack the architect of the reforms, said at a Downing Street press conference following talks with Spanish counterpart Mariano Rajoy: "I think Andrew Lansley is doing a very good job.
"I have worked with him for many, many years and I think he understands the health service better than almost anyone else in Parliament and does a very good job and he has my support."
Mr Cameron said reform "always involves argument" but he was confident the Government could win the arguments and show the changes would improve the NHS.
Mr Cameron said reform was "never easy" but it was "vital" the plans were put in place.
"I think it is important we stand back for a moment and try to explain again to people what it is we are attempting to do because I think the principle behind the reforms does actually have quite good support," he added.
"For years, people have said there is too much bureaucratic decision-making in the NHS, we want clinical decision making. That's what the reforms deliver."
Meanwhile, Education Secretary Michael Gove denied being one of the three Cabinet ministers reported to have expressed their concerns about the Health and Social Care Bill to the website ConservativeHome.
Mr Gove told a Westminster lunch he was "absolutely" in favour of the reforms contained in the Bill and praised Mr Lansley for being "brave and right and principled in pressing ahead with it".
"I do not think - and I have not said to anyone - that we should drop the Bill," said Mr Gove.
Latest opinion polling suggests the row over the Bill may be damaging the coalition.
More than two-thirds of people do not trust the Government's handling of the NHS, according to a survey commissioned by BBC 5 Live's Victoria Derbyshire programme.
Just 18% of adults surveyed in England think Mr Lansley is doing a good job as Health Secretary.
An ICM poll for The Guardian found that 52% believed the Health and Social Care Bill should be dropped, against 33% who said the Government should press ahead with the legislation.
Deputy Prime Minister Nick Clegg defended the reforms earlier, insisting the Bill had been changed "very considerably" since a pause in the progress of the legislation through Parliament last year.
"I am a Liberal Democrat and I care passionately about the NHS. If I felt that this legislation would lead to the privatisation of the NHS, as the critics claim, if I felt that this legislation would lead to the ruin of the NHS, of course we would drop it," he told ITV's Daybreak.
"The truth is that at the heart of this legislation is a very simple straightforward idea and it is this: it is to give people who know patients the best - doctors, nurses and clinicians - more say about what happens to those patients and how the NHS is run.
"I think that basic, simple idea is a good one."
Despite amassing 154,146 signatures, a petition calling for the Bill to be dropped altogether cannot be debated by the Commons at present after no MP took up the case this afternoon.
Any e-petition on the Government's official website which reaches six-figure support is eligible to be put to the Backbench Business Committee as a potential topic for parliamentary time.
At the committee's weekly meeting this afternoon it was not proposed by any MP, meaning it cannot yet be considered.
Asked whether the Government remained open to amending the legislation, the Prime Minister's official spokesman said: "I would not envisage significant changes to the Health Bill.
"Clearly, it is being debated still in the House of Lords and I would not want to prejudge those discussions.
"But we had a listening exercise, we took account of the views and we amended the legislation."
:: ICM Research interviewed 1,013 adults aged 18 and over by telephone between February 17 and 19. ComRes conducted its survey of 1,005 adults across England between February 17 and 19 2012.
Labour MP Jonathan Reynolds has submitted a written bid for a debate on the petition to the committee, a spokesman said.
But he will be expected to attend in person at next week's session and faces a tough battle to secure any time.
There are a limited number of slots available and the fact that the legislation is being debated by Parliament at present will be considred as a factor.
PA
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