Speaking on Radio Four's Today programme on Thursday, Mr Lansley said that Labour's four-year plan to save £20bn implied ‘efficiency savings' of around 3-3.5%.
He added: ‘Of course we need to do that. And we may need to do more because we have increases in demand in the NHS and a need to improve the outcomes.
‘Every penny saved is a penny which can be reinvested.'
The new coalition government agreement published on Wednesday commits the new administration to real-terms funding increases for the NHS.
Dr Peter Carter, RCN chief executive and general secretary, said: 'There will be tough times ahead for the NHS and we all have a part to play in ensuring we get value for money for our health spending. Nurses wish to work with the government to deliver fresh thinking on how savings can be made while protecting patient care.
'When looking at NHS funding the guiding principle must be the protection of frontline services to ensure patients receive the highest possible standard of care.'
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