Speaking to Sky News, the health and social care secretary repeated Theresa May’s comments that a “Brexit dividend” will contribute to the increase, and insisted the rise would “not depend on this or that level of economic growth”.
He said Chancellor Philip Hammond would reveal more details in the autumn budget in November.
It comes as the prime minister, who is coming under pressure over her announcement to mark the NHS’s 70th birthday, is due to give a speech in north London.
Mr Hunt dismissed findings from the Office for Budget Responsibility and Institute for Fiscal Studies that said there would be a net cost, not a dividend, from Brexit.
“What there’s debate about is what’s going to happen to the economy over the next five to 10 years,” he said.
“They would be the first to say some forecasts in the past have been wrong and I think most people think the British economy’s been a lot more resilient than predicted at the time of the referendum.”
The 3.4% hike is broadly in line with a suggestion from the Institute for Public Policy Research (IPPR) think tank, Mr Hunt added.
The report he referenced called for a rise of 3.5% and said that £10bn was needed simultaneously for social care by 2030.
It called for this to be funded by a 1% rise in national insurance contributions.
Mr Hunt promised he would “come forward” with a “long-term plan” for the social care system.
He said he was “absolutely confident” the government could fund its commitment and insisted: “This is not going to be something that depends on this or that level of economic growth.”
One of the funding sources will be “through the taxation system”, he confirmed.
Historically, every year since the NHS was created, the amount of money it receives over the top of inflation has increased by 3.7%.
The prime minister is facing a backlash for linking her NHS cash boost with the Vote Leave pledge during the referendum campaign to spend Britain’s EU contributions on the health service instead.
The £350m emblazoned on the side of a battle bus and promoted by now foreign secretary Boris Johnson has been repeatedly criticised by the UK Statistics Authority as being “misused”.