In a speech setting out his stall to become leader of the Conservative party, justice secretary Mr Gove pledged to 'honour the instructions the British people have given us' in the EU referendum vote.
The controversial Brexit campaign pledge that the NHS could receive a £350m windfall if the UK left the EU has been heavily criticised, with former health secretary Lord Lansley warning earlier this week that it was 'never remotely correct'.
But Mr Gove said that under his leadership, the Conservatives would deliver on 'the promise to use the money that we currently send to Brussels and invest it instead on the priorities of the British people, principally in the NHS'.
Mr Gove said: 'Our most important public service will always be the NHS. I want to say something clear and unambiguous about my commitment to the NHS. The government has got to invest more money in our NHS.
'The people who work in it are heroic - they do an amazing job. But we need to face the fact that we need more money to deliver Jeremy Hunt's absolutely correct drive to guarantee even better standards of care. I will take all the steps necessary to give the NHS at least another £100m per week by 2020.'
At the Health+Care conference in London this week, Lord Lansley warned that the need for increased NHS funding was 'inescapable'. But he criticised the £350m NHS funding pledge made during the Brexit campaign, warning that the maximum amount of funding that could be generated by leaving the EU would be around £120m.