The Morrison government will have a system in place within weeks to support the resumption of international travel as vaccination rates rise, the trade minister, Dan Tehan, says.

With senior federal ministers meeting on Wednesday to continue work around vaccine passports, Tehan told reporters the resumption of international travel would require “a system that can enable recognition of vaccination – a vaccination certification scheme”.

“We’re in the process of planning that so that in the coming weeks we will have a system up and ready so when we hit that 70% or 80% vaccination mark Australians will be able to travel overseas again and also Australians will be able to return home in greater numbers,” Tehan told reporters in Canberra.

“We’ll also be able to start welcoming international students, those who want to come here to work, ultimately tourists again.”

The four-phase plan for reopening Australia unveiled by Scott Morrison at the end of July suggests vaccinated Australians would be able to head overseas again more freely when at least 80% of the over-16 population had been fully vaccinated.

Under “Phase C” of the plan, governments would abolish caps on vaccinated Australians returning from overseas, and lift all restrictions on outbound travel for vaccinated Australians.

The triggers are linked to vaccination rates rather than a fixed date, although the New South Wales premier, Gladys Berejiklian, has been signalling international travel will probably resume in the state in time for Christmas.

Tehan said the government was working to develop a QR code with the International Civil Aviation Organisation so the vaccine certificates would be internationally recognised.

Similarly, QR codes would be integrated with state check-in apps to allow Australians to demonstrate their vaccination status to attend events including sport and theatre, he said.

“This is all part of our plan to open the economy and open the country safely.”

Berejiklian has signalled repeatedly in recent weeks the state will facilitate more normalised international travel once the agreed vaccination thresholds are met.

Morrison said last week it was possible international travel could resume in NSW ahead of other states, because NSW was ahead of other jurisdictions in terms of vaccination rates.

National cabinet – which includes Morrison, the premiers and the chief ministers – received an update last week from former health chief Jane Halton on a review of quarantine arrangements.

That included the “need for risk based approaches to quarantine and South Australian home quarantine trial”, according to Morrison’s statement after the meeting last week.

“Both pieces of work will assist national cabinet’s consideration of modifications to Australia’s quarantine systems at Phase B and C of the national plan.”

Over the past few weeks, the federal government has been campaigning hard for all states and territories to proceed to the next stages of the opening-up plan when the next two thresholds are met: 70% and 80% of over-16s fully vaccinated against Covid-19.

But many observers and state and territory leaders have pointed out the plan is more nuanced than how some federal government figures have presented it. The plan, agreed by national cabinet in July, was always “subject to change if required”.