Labor has sparked a political fight over the private health insurance rebate claimed by millions of Australians, refusing to rule out changing the policy after declaring it will “look at” the scheme if it takes power at the next election.

The new signal puts families on notice to watch for changes to the $6.4 billion annual assistance under a Labor government, amid calls to scale back the rebate to boost the budget bottom line.

The new remarks triggered “great concern” among the private health insurance industry, which is calling on Labor to outline a “Plan B” for households and insurers if the rebate is scaled back.

The private insurance sector has expressed concern at the refusal of King and Shorten to back the rebate in its current form. Credit:Alex Ellinghausen

Opposition Leader Bill Shorten yesterday accused the private health insurers of “running amok” with their price increases, days after new figures showed premiums were rising 3.95 per cent on average across the sector.