Friday’s day of action by public servants around the country has been declared a flop by the Commonwealth workplace authority.

But the union behind the action has returned fire, saying Public Service Commissioner John Lloyd  was trying to mislead about the strike.

Only 730 Tax Office public servants, from a workforce of nearly 20,000, stopped work, according to Mr Lloyd.

Mr Lloyd described the action, organised by the Community and Public Sector Union, as “subdued”, attracting the support of fewer public servants than previous efforts and said the impact on government services was minor.

The strike was part of a broader protest across federal government departments and agencies whose workforces have been in dispute with the Coalition government over wages and conditions for more than three years.

But at the giant Department of Human Services, the largest Commonwealth employer, about 5000 public servants, from a workforce of 34,500, participated in the action and only one site had to close, Mr Lloyd said.

The commissioner said the Department of the Environment and Energy had only 36 of its 2400 employees participate, with no impact.

In the Department of Parliamentary Services, only 27 of its 894 employees participated, again with no impact to services, according to Mr Lloyd.

“In the Department of Immigration and Border Protection, including the Australian Border Force, less than 4 per cent of its 13,500 employees participated,” he said.

“Impact on services was low.”

The commissioner called on those public servants still resisting the Coalition’s industrial relations policy to submit to the offers made by their departments.

“The union leaders’ calls to create industrial havoc and inconvenience the public have fallen flat. Some union members must wonder why they are losing another day’s pay,” Mr Lloyd said.

“The best course of action would be to engage in constructive bargaining to finalise enterprise agreements which offer pay rises for the next three years.

“The path of industrial action continuously fails to move the bargaining agenda one iota.”

But CPSU national secretary Nadine Flood said she did not know where Mr Lloyd got his figures.

“Thousands of our members went on strike on Friday,” the union leader said.

“I don’t know what the Public Service Commissioner’s numbers are based on but there are more people in some of our social media photos than the total numbers he’s quoting.

“John Lloyd is being particularly misleading by referring to participation by staff from Immigration and Border Protection, given they were not part of last Friday’s 24-hour strike.

“A small number of workers took limited three-hour action to join a delegation to ministers’ offices but there was no 24-hour strike and never any intention for a large-scale strike in DIBP at that time.

“Public sector workers strike and vote no to agreements not because the CPSU tells them to but because the agreements being pushed under the Turnbull government’s bargaining policy strip away workplace rights and conditions.”