The prime minister said contributions will rise “a bit”, but delayed further details until the autumn budget.
She promised the contributions would be calculated in a “fair and balanced way”.
Speaking at the Royal Free hospital in north London, Mrs May also repeated her claim that a “Brexit dividend” would help foot the bill.
“We cannot continue to put a sticking plaster on the NHS budget each year,” she said.
“So we will do more than simply give the NHS a one-off injection of cash…
“This must be a plan that ensures every penny is well spent.
“It must be a plan that tackles wastes, reduces bureaucracy, and eliminates unacceptable variation, with all these efficiency savings reinvested back into patient care.”
On who would be hit by more tax rises, Mrs May pledged she would “listen to views about how we do this”.
Asked by Sky News when patients could expect to see improvements in NHS care, the prime minister did not give a time frame.
She said she wanted to see better mental health services and cancer survival rates.
Jonathan Ashworth, Labour’s shadow health secretary, said the money announced on Monday was “not enough to save our NHS” after eight years of austerity.
“People are waiting longer and in pain because of Tory cuts to the NHS,” he said.
“The prime minister couldn’t say today when this will improve and waiting lists will come down.
“If the Conservatives do manage to publish the detail of their insufficient 3.4% increase, then Labour’s fully costed plans to raise taxes for the top 5% and big business will top up NHS spending growth to around the 5% which is needed.”