Speaking at the King's Fund in London, he said 'the NHS is our preferred bidder' and services should only go out to tender where existing providers have failed repeatedly.
Asked to clarify his comments, the health secretary said he had been in talks with unions and agreed there was a need for greater clarity.
Last month, Unite presented a letter signed by 3,000 NHS members calling on the health secretary to halt the privatisation of the health service.
A second phase of the BMA anti-marketisation campaign will also begin soon, aiming to inform the public about use of the private sector in the NHS.
Unite national officer for health Karen Reay said Mr Burnham's speech 'appeared to indicate a softening of the pro-privatisation rhetoric'.