The forecasts for wages growth in the Turnbull government’s budget are already in doubt, with new data showing Australian wages are struggling to grow above an annual rate of 2%.

Bureau of Statistics figures show wages grew by just 0.5% in the March quarter, keeping the annual rate at 2.1% in seasonally adjusted and trend terms.

It means national wages will have to grow by 0.7% over the next three months to keep alive the government’s budget forecasts for 2017-18.

The budget predicts wages will grow by 2.25% in the 2017-18 financial year, and economists raised doubts about the forecast from the moment the budget was released last week, wondering if it was too optimistic.

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The budget forecasts wages will grow at 2.25% this financial year, then 2.75% in 2018-19, followed by 3.25% in 2019-20 and 3.5% in 2020-21.

Australian wages have been stuck at an annual pace of 2.1% for the past nine months, after lifting slightly from a historically low 1.9% last year.

The shadow treasurer, Chris Bowen, speaking at the National Press Club on Wednesday, said the budget’s wage forecasts were “problematic” and since budget surpluses are dependant on wage forecasts the government’s surplus plans may face early pressure.

He said low wages growth, which was an international problem, was affecting the living standards of all Australians, and Labor was working on a wages policy.

“It’s not all the fault of the government and it’s not all entirely Australian issues,” he said.

“Of course, there’s an international phenomenon going on here, but I think that any government that just says ‘oh, it’s all too hard and people won’t have wages growth’ is giving up on one of our core responsibilities.”

The ABS data shows private sector wages grew by 1.9% and public sector wages grew 2.3% through the year to March.

The ABS chief economist, Bruce Hockman, said the March-quarter wage growth continued a period of “subdued first-quarter rises”.

National wage growth was primarily driven by regular increases in the education and training and healthcare and social assistance industries.

In the private sector, the public administration and safety industry recorded the lowest growth over the quarter (0.1%). The education and training industry recorded the highest quarterly rise of 0.9%.

In the public sector, professional, scientific and technical services recorded the lowest quarterly wages growth of 0.2%. Education and training recorded the highest quarterly rise of 0.8%.

The figures come as the Australian Council of Trade Unions has defended its claim for a 7.2% minimum wage rise as the Fair Work Commission concludes hearings for a wage rise to take effect from 1 July.

In the FWC hearing on Tuesday, the ACTU criticised the federal government for arguing the transfer system was a better way to help low-paid households.

The ACTU wanted to know where the money was in the 2018 budget, arguing “all we have is the promise of a little under $10 a week for lower-income workers but it comes with a catch – a big one – that it is contingent on locking in tax cuts for higher-income earners over years to come”.

The ACTU noted many employers had asked for a 1.9% increase, a wage freeze, while others had asked for real cuts: AiGroup (1.8%), the Master Grocers Association (1.1%) and Restaurant & Catering Industrial (0%).

“It’s also worth remembering that, since business tax cuts started working their way through the system, award reliance increased,” the ACTU representative said.

“We’ve got lower business taxes for many award-reliant employers and, in response, more of them are paying the lowest legal rate of pay they can to their employees and asking that their wages either be frozen in real terms or cut. These employers will not raise wages unless they are forced to. And the panel should force them.”