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Mr Hague took part in a political panel at the South GP CME 2014 general practice conference.
The Green Party disagrees with likely coalition partner Labour, which has been criticised for promising universal primary health care to older people, a group with lower poverty levels than younger groups.
The Greens would give free primary care to those aged up to 18, after which targeted assistance would help those on lower incomes.
Those who could afford it should pay more towards their health care, Mr Hague said.
The Greens would increase funding for primary and public health.
Those who claimed there was insufficient money should consider the 2010 tax cuts, which cost $1.1 billion every year, Mr Hague said.
Earlier, the panel got off to a disjointed start because of the late arrival of Mr Hague and National health spokeswoman and Associate Health Minister Jo Goodhew, who were delayed on the same flight.
At the start, just Labour's Dr David Clark, and United Future leader and Associate Health Minister Peter Dunne took the stage and Dunedin-based National List MP Michael Woodhouse was observing in the audience.
Mr Woodhouse very briefly took the stage to fill in for his absent colleague, who then arrived to take her place.
Labour would reduce the ''huge gap'' between the rich and the poor, something Dr Clark felt was holding the country back.
''Governments of both stripes have not, in my view, addressed it properly.''
By dropping ''expensive policies'' such as removing GST from fruit and vegetables, Labour could afford measures such as free primary health care for older people.
Labour was targeting younger people as well as older people, he said when asked if it was fair for the older group to receive free primary health care.
Mr Dunne said he wanted to see the country adopt an ACC-style health insurance system, to cope with future cost pressures.
Mr Dunne said Labour's health spending promises were unaffordable.
Mrs Goodhew said the Government made no apology for pushing health targets, which had driven success in areas such as emergency department access and vaccinations.
Unlike many other countries, the Government had increased health funding in the face of the financial crisis and its aftermath.
A medical student in the audience asked about the fact graduate medical students faced an uncertain job market, while being in debt to the tune of $100,000.
In response, Mrs Goodhew said the medical jobs market had become tighter, but the sector was working hard to ensure as many positions were available as possible.
''It's a changing global situation around employment.''
• Labour also released its full health policy yesterday. Under the policy, the focus would shift from ''narrow targets and and short-term thinking'' towards public health and prevention, health spokeswoman Annette King said.
Policy initiatives included a national bowel cancer screening programme and a review of ambulance services.