Leaving the European Union would allow the UK government to spend an extra £100m a week on the NHS by 2020, leading Brexit campaigners have said.
Justice Secretary Michael Gove called on the government to pledge the money in the event of an EU exit - saying it would come from the UK's EU budget.
It comes after Mr Gove took part in a televised Q&A, urging voters to "take back control" from "Europe's elites".
The Remain campaign described the NHS spending claim as "totally dishonest".
Greg Hands, chief secretary to the Treasury, said: "Doctors and nurses want to stay in Europe because they understand that quitting the single market would damage the NHS by shrinking the economy.
"It is totally dishonest to pretend there would be more to spend on the NHS when all credible economists agree we'd have billions of pounds less."
On Friday, Mr Gove took part in a live Sky News interview, arguing the case for Brexit. He said leaving the EU would lead to more jobs, a "non-racist" immigration policy and would allow the government to help the steel industry.
It followed Thursday night's show which had a similar format but featured Prime Minister David Cameron, who is campaigning for Remain.
Mr Gove criticised the prime minister's performance, describing it as "depressing" and "an exercise in trying to scare you".
Challenged on the lack of international leaders and organisations backing the Leave campaign, he said the public had "had enough of experts" saying "they know what is best and getting it consistently wrong".
He was also pressed on his campaign's controversial claim that £350m a week is spent on the EU.
Questioned on the figure, Mr Gove said he was "happy" to have the claim independently audited and described it as "the difference between the total amount we hand over and what we get back".
The important thing, he said, was "we don't have control of that money".
The justice secretary described the EU as a "job-destroying machine" but also said: "I can't guarantee every person currently in work in their current job will keep their job."
Shadow justice secretary and Remain campaigner Lord Falconer said the interview was a "lost opportunity" because Mr Gove had not explained "the economics of leaving".
Meanwhile Nobel Prize-winning economist Professor Amartya Sen warned Europe was likely to act like a "jilted suitor" if Britain left the EU.
He told BBC's This Week's World the Vote Leave the argument Britain can flourish outside the EU was "simply mistaken" and was based on "pretty bad economics".
The Electoral Commission also announced polling cards were wrongly sent to at least 3,462 EU citizens who are not allowed to vote in the EU referendum.