The cost of seeing a doctor would soar if private health insurers were allowed to cover GP fees, a health economist has warned. And consumer advocates say such a change would erode the universal access to basic healthcare supposedly guaranteed by Medicare.

Health Minister Peter Dutton on Friday opened the door to lifting the long-standing ban on private health insurers paying for GP services.

Peter Dutton: Change unsustainable. Credit:Sean Davey

''I want every Australian to have a good relationship with their GP, so I wouldn't rule out any changes,'' Mr Dutton said in a statement.

The nation's largest health insurer, Medibank Private, has been pushing for several months for the change, arguing that treating medical conditions at an earlier stage would reduce the need for more expensive hospital treatment later.