Jeremy Hunt has called for a 10-year funding deal for the NHS amid speculation the Government could back a ring-fenced tax rise to provide a cash boost.
The Health and Social Care Secretary said a long-term deal would allow proper planning to train the staff needed to cope with the challenges of Britain's ageing population.
He said the possibility of a tax earmarked for the NHS was popular with voters - but only if they were convinced there was going to be reform.
In a sign the argument within Government may be going in that direction, the Sunday Times reported that Theresa May will back extra NHS spending - and a senior Cabinet source told the newspaper a special tax is "still on the table".
The announcement of a multibillion-pound increase in funds could be timed to coincide with the 70th anniversary of the NHS in July.
But Mr Hunt told ITV's Peston on Sunday it was "premature" to speculate that a £4 billion-a-year boost will be announced.
He said: "There's no doubt that NHS staff right now are working unbelievably hard and they need to have some hope for the future, but their real concern is this rather crazy way that we have been funding the NHS over the last 20 years - which has basically been feast or famine."
The ageing population meant that in 10 years' time there will be a million more people aged over 75, he said.
"The question is: do we want to approach that challenge in a strategic way where we move beyond this feast or famine and look at it in a structured way, and I think, if we do that, we will get a much better deal for taxpayers and be much fairer to the staff on the NHS."
Chancellor Philip Hammond has announced a full departmental spending review will take place next year, but Mr Hunt argued that health should be treated differently with a longer-than-usual 10-year settlement.
Mr Hunt acknowledged "that isn't government policy" but "given that it takes seven years to train a doctor and three years to train a nurse, you need to have something that gives you the ability to look ahead".
Asked about the potential for an earmarked NHS tax, Mr Hunt said: "It's a bit premature to talk about that.
"If you ask the public about the NHS, they are very clear that they would like to see more money going to the NHS, they would be prepared to see some of their own taxes going into the NHS, but they are very clear they want to know that money is actually going into the NHS and social care system.
"They want to know that the NHS is going to reform, tackle some of the inefficiencies."
Mr Hunt has suggested an increase in tax could avoid the political calamity over social care funding that hit the Tories during the general election campaign, when Mrs May was forced into a hasty U-turn over a package of reforms dubbed the "dementia tax" by critics.
He told the Mail on Sunday: "It is beyond dispute that with a million more over-75s in 10 years' time, the NHS and social care system are going to need more money.
"The public are very clear that for that specific issue they are willing to pay more tax, but want to know that every penny is going to be spent wisely."
Asked if the appeal of such a ring-fenced tax was that it would guarantee money to help the elderly and infirm, Mr Hunt said: "Absolutely. That is the attraction."
A 1p rise in income tax could raise around £5 billion to help fund the health and care system.
"No one can deny we got our fingers burned on social care in the election," Mr Hunt said.
He added that "if we want every single old person to be treated with the dignity and respect we would want for our own mum or dad, it will need more resources."
But he acknowledged the idea of specifying what a tax could be used for could meet resistance in Whitehall: "The Treasury do not like it because it takes it out of their hands."