Human rights lawyers say enough is enough after last week's decision to cut arrivals in half, complaining the rules have been skewed to benefit the wealthy while leaving those most in need unable to share the last days with dying family members.

Federal cabinet ministers could not be drawn into giving a timetable for those families nor nominate a threshold of vaccinated Australians for the government to reconsider current restrictions.

NSW Premier Gladys Berejiklian nominated 80 per cent, while federal Liberal MP Tim Wilson suggested a rate of 60 per cent to begin opening up restrictions on international travel.

Health Minister Greg Hunt and Treasurer Josh Frydenberg offered no targets when questioned by reporters.

"We will open the borders when it is safe and that is why the vaccination rollout is important and that is why it is pleasing to see more people getting vaccinated each and every day," Mr Frydenberg responded on Monday.

Mr Hunt said it was understandable for people to have opinions, but the government's approach had been to follow the medical advice. The Doherty Institute was working on threshold advice, he confirmed.

Last week was the national's most successful since the vaccine rollout began with more than 880,000 doses administered across Australia throughout the week.

More than 30 per cent of all eligible Australians aged over 16 have now had at least one dose.

For the first time, more second doses of the vaccine were administered in the most recent 24-hour snapshot than first doses.

But after the international arrivals cap was halved last week, and record vaccination numbers after under 40s were told they could ask for AstraZeneca doses, business leaders began pressing the government to set firm vaccination targets to reopen international borders.

Australia's travel restrictions has also been subject to an investigation by the national audit office, along with the effectiveness of human biosecurity practices at international airports through the pandemic.

The Human Rights Law Centre told the watchdog that the "arbitrary and inconsistent rules" must be reassessed to more fairly prioritise between international arrivals.

Josephine Langbien from the centre said the reality is that international travel is still allowed for people in business, politics and events, but the complex web of restrictions and exemptions had left many families indefinitely separated.

"The strain on people separated from their loved ones cannot be underestimated and must be addressed," she said.

"While wealthy investors and people on business trips are allowed to travel, many people cannot see their parents, their fiancé, their brother or sister if they are not Australian residents."

The centre urged the government to focus on helping people reunite with their loved ones quickly and safety.

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Sophie Robinson, an audiologist from the UK who came to live in Canberra on a skilled migrant visa to fill a local shortage, has been trying to get an exemption for her mother to come help her after giving birth to a daughter four months ago. This month her bid was rejected. She has begun the process of trying again.

"A lot of people have said any exemptions that are being approved are only for one parent anyway; it's completely impossible to get both parents and so I've only been applying for my mum."

Both she and her husband have had their second vaccine dose, making the option to move to the UK and abandon life in Australia a little bit easier to swallow.

"That doesn't worry me now because I feel like the UK is a much safer place to be than it has been, and potentially they've gone back to normal life.

"I just can't see how we can stay in Australia. Without my parents meeting my baby for such a long time ... it's like we're being forced out."

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