Australia’s childcare costs have risen at five times the rate of inflation over the course of a year, with the average hourly fee increasing by 7.6%.

The education minister, Simon Birmingham, said data released on Sunday showed the Turnbull government’s “temporary stop-gap” measures are not enough to ease childcare costs, with more action urgently needed.

The Early Childhood and Childcare in Summary report found more than 1.2 million children were in childcare in the June 2016 quarter. This was 2.1% more than a year earlier.

The average hourly fee for all childcare service types was $8.65, an increase of 7.6% since the June 2015 quarter, the report said.

In long day care – by far the most popular service – average hourly fees increased by 6.3% to $8.90.

In a statement responding to the report, Birmingham made the case for the government’s proposed childcare overhaul, which is tied to a swag of welfare cuts.

The reform plan includes an hourly rate cap which is a necessary first step to arrest fee increases that would also provide families with a reference point, Birmingham said.

Under the plan, the $7,500 childcare rebate limit would also be removed for all families earning less than $185,000, he said.

“Over the next two weeks parliament has the opportunity to step up to the plate and provide the support that Australian families are crying out for,” he said.

On Sunday, Birmingham said the opposition leader, Bill Shorten, should stop talking with a “forked tongue” on childcare and back the government’s reform package at a time of escalating fees.

But the opposition leader says that, while clearly there is a problem in the childcare sector, he won’t be “bullied” into something that is “robbing Peter to pay Paul”.

Birmingham has declined to speculate on the progress of getting the government’s childcare package through the parliament but says new data showing rising costs for parents paint a “disturbing picture”.

“Stop blocking the actual solutions that are on the table, and to actually support us to pay for the reforms that can invest more in childcare, keep a lid on price growth, and make it more affordable and available for Australian families,” the minister told reporters in Adelaide.

Shorten said there was clearly a childcare problem with fees going up, which was becoming a disincentive for people to return to work. But he said it was not good enough for the prime minister, Malcolm Turnbull, and his government to blame someone else for four years of inaction on the issue.

“Why does he want to link improvements to childcare to cuts to family benefits?” he said in Melbourne. “If Mr Turnbull wants to pay for the childcare reforms he can drop his unsustainable $50b worth corporate tax giveaway, it’s as easy as that.”

The deputy prime minister, Barnaby Joyce, said if the parliament stymied the package it would be on the shoulders of the Senate and Labor as to why families were not looked after. He said the government was taking prudent measures while assisting families

“We have to get the budget back into balance,” Joyce told ABC television. “If we don’t get this under control, then in 10, 15, or whatever years’ time, we won’t have support for childcare because we won’t have any money.”

Labor has claimed pensioners, families, new mums and young Australians will be hurt by welfare cuts that would be used to support the reform.