The federal government has approved private health insurance premiums increasing amounts to an average of 3.03% this year, but already one major insurer has said their prices will rise by 4.1%.

The private health industry has defended the rise as being below inflation and similar increases to other insurance products, but said costs to private health facilities like wages, staffing and cybersecurity were also on the rise.

The health minister, Mark Butler, on Tuesday announced the annual rise in private health premium, three weeks before the price changes come into effect on 1 April. He said the 3.03% increase, which was the average rise across the sector, was lower than annual rises in inflation and wages, and had decided after “considering [insurers’] years of record profits”.

“While we know that any increase will be hard to bear during a global cost-of-living crunch, the Albanese government has ensured that health insurance premiums will fall relative to Australians’ wages,” Butler said in a statement.

Insurers had reportedly asked for an annual increase as high as 6%, a number Butler had rejected late last year. Private Healthcare Australia, the industry peak body, has been contacted for comment.

Butler last week shrugged off criticism from the Coalition for not having announced the increase earlier, saying it was “not unusual at all” for such decisions to be made in early March.

On Tuesday, he said individual insurers have a “responsibility to clearly explain to their policyholders any changes to their premiums”.

While the minister painted the government’s decision as a response to cost-of-living concerns, the first insurer to announce an individual increase, NIB, said its premiums would rise by an average 4.1% – above the average outlined by Butler.

It came after Butler’s statement outlined “wages rising by 4.2% and inflation increasing by 4.1% in 2023” – meaning NIB’s premium rise was on par with wages and inflation increases.

In an announcement to the Australian Stock Exchange, NIB’s chief executive, Mark Fitzgibbon, said the increase reflected “the return of hospital and ancillary treatment post Covid-19 and a rise in health and medical treatment costs”.

Fitzgibbon said that “inflation has moved back to long-term trends and it’s crucial that insurers are able to price for this”. The insurer noted its previous increase in 2023 and 2022, 2.72% and 2.66%, were its two lowest increases in the past 20 years.

Fitzgibbon denied insurers were “sitting back passively responding to inflationary pressure by just lifting premiums”, saying NIB offered health and wellbeing programs as well as other health management.

Medibank announced a 3.31% increase, also above Butler’s industry average, but below what the company said was the industry’s 10-year average of 3.8%.

“We know many households are doing it tough at the moment, and our focus has been to balance the impact of rising health costs with the need to keep premiums affordable for our customers,” said Medibank’s chief customer officer, Milosh Milisavljevic.

“Premium increases are never welcome, which is why we have worked hard to ensure this year’s is as low as it can be, despite rising health costs in the private system. “

Medibank’s increase applied to Medibank and AHM products.

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The shadow health minister, Anne Ruston, accused the government of having “shamelessly delayed” its announcement on increases to private health insurance premiums until after the weekend’s Dunkley by-election.

In a statement to Guardian Australia, Ruston claimed it was “the price hike the Government wanted to hide.”

“It is the longest Australians have had to wait in 15 years to find out how much more they will need to fork out for private health insurance,” he claimed.

“We also know that this is only an average industry price increase, so some consumers will be paying substantially more than the increase announced today – with less time to budget or shop around.”

Private Healthcare Australia CEO Dr Rachel David said health funds “don’t want to increase premiums by a single dollar”, but claimed they couldn’t avoid it, pointing to rising costs and increasing consumer claims.

“Both hospital and extras claims have skyrocketed in the past year, exceeding pre-pandemic levels. The latest APRA data shows in the year to December 2023, health funds paid a record $23.6 billion for claims – 10% more than the previous year,” David said.

“In the current economy, it is becoming more challenging to keep private hospital care sustainable without increasing premiums.”

David called on the government to reduce costs of medical implants and surgical supplies, and remove funding for “low value care and harmful medical devices” – claiming such reforms could help reduce consumer costs.

The Australian Private Hospitals Association (APHA) said increased premiums must help ensure the sustainability of private hospitals. Its chief executive, Michael Roff, called on private insurers to help support the sector and “not profit”.

“The onus is now squarely on the health insurance companies to ensure the ongoing viability of Australia’s private hospitals following today’s premium increase announcement,” the APHA said in a statement.

Roff said private hospitals were facing workforce pressures and rising costs, claiming some facilities had been forced to close. He said health insurers were “experiencing record profitability and clearly have the capacity to come to the aid of hospitals”.

“Unfortunately, we will continue to see private hospitals close or reduce services unless health insurance companies put sustainability of the private health sector before their own profits,” Roff said.