The Australian Council of Trade Unions is becoming “increasingly concerned” about the pace of the federal vaccine rollout, pleading with the government to urgently immunise the many thousands of aged and disability care staff who have been waiting months for a jab.

“We are concerned that the current rollout plan seems to have abandoned or deferred plans to have in-reach workplace vaccinations available for all workers in aged care and disability support,” ACTU assistant secretary Liam O’Brien wrote in a letter to Health Minister Greg Hunt.

In a Senate hearing on Tuesday, health department officials could only confirm 37,000 aged-care staff had been vaccinated so far as part of in-reach programs in residential care homes.

The actual number is likely far higher, as the federal department did not have oversight of staff who may have been vaccinated at GPs, but many tens of thousands of staff in aged and disability care are likely to still be waiting for jabs.

Health department associate secretary Caroline Edwards admitted the federal government couldn’t put a number on the outstanding vaccines, but said the department was “still working with the sector” to improve reporting and record keeping in that respect.

Unions are urging Greg Hunt to speed up the rollout. Photo: AAP

Last week, in another hearing, the department admitted barely six per cent of disability care residents had received even their first shot of the two-dose vaccines – despite saying they were among the “highest risk population”.

The ACTU has told Mr Hunt of its alarm at the figures.

The federal government originally planned to give all 678,000 high-risk workers and care residents in Phase 1a of the vaccine rollout their vaccinations within six weeks of the program starting, but has now been running for nine weeks with no end in sight.

“The union movement has become increasingly concerned about the ability of the vaccine rollout to meet its central task – protecting the most vulnerable members of our society from a virus which has killed hundreds here and millions worldwide,” Mr O’Brien wrote.

“To date we believe less than 10 per cent of workers in these sectors have been vaccinated, and those that have been vaccinated have done so through GPs and not, as was outlined in your plan, through the in-reach workplace vaccination program.”

Unions are questioning the rollout in aged care. Photo: AAP

Mr O’Brien said the ACTU hoped to see the “public release of a comprehensive plan” for vaccinating aged and disability workers, including mass vaccination centres, at-work vaccinations, plus an “urgent” public awareness campaign.

“Currently workers in these sectors have no idea when, or how, they will be able to access the vaccines,” Mr O’Brien wrote.

The ACTU is also calling for daily reporting of numbers of workers vaccinated.

The federal government has not been able to provide specific numbers of how many people in each phase of the rollout have been immunised, but the total figure ticked over two million doses on Wednesday.

“These workers have been told time and again they are in the highest priority group. They deserve to know that they and their colleagues are getting the vaccine as fast as possible,” Mr O’Brien wrote.

Unions have also called for paid leave for workers to give them time to get vaccinated.

Ms Edwards said on Tuesday the department would begin to “ramp up” vaccinations in aged and disability care this week, including the first of 13 “pop-up clinics” focusing on workers.