Australian Prime Minister Scott Morrison says he's discussing the opening of the trans-Tasman border with Prime Minister Jacinda Ardern.

Morrison said he had discussed the possibility of easing stringent travel restrictions across the Tasman, as both countries were on "similar trajectories" in their response to Covid-19.

He said New Zealand had put in place far greater restrictions to combat the virus, a reference to the four-week lockdown, and Australia's response had been "the same, if not better".

"Now if there is any country in the world with whom we can reconnect with first, undoubtedly that's New Zealand," he said.

JAMES MORGAN/GETTY Another rendezvous? New Zealand Prime Minister Jacinda Ardern and Australian Prime Minster Scott Morrison during a bi-lateral meeting on the day New Zealand confirmed its first Covid-19 case. A reopening of the trans-Tasman border is an option being explored, Morrison says.

READ MORE:

* New Zealand's travel bubble could include Australia and Singapore

* Coronavirus alert levels: When can I travel around New Zealand?

* Coronavirus: Trans-Tasman 'bubble' could ease travel restrictions

* Coronavirus: Air New Zealand's big regional problem

"There already are exemptions the border force commissioner has ... That's something that we will just work through carefully."

Ardern said earlier this month she was open to the idea of the easing of travel across the Tasman but "we're not in the position to even be having that conversation yet".

A spokesman for the prime minister on Thursday confirmed the conversation had now happened, with the pair discussing the future of the trans-Tasman border, "but no plans have been confirmed".

The border restrictions and quarantine order for people entering the country would only be lifted when "we are confident it is safe to do so".

"So while nothing is going to happen immediately, the idea has merit as something that might be possible down the track," the spokesman said in a statement.

When talking a week ago about relaxing travel restrictions, Ardern said discussions were underway with Singapore.

SAM MOOY/GETTY IMAGES Prime Minister Scott Morrison has said New Zeland and Australia may be able to relax border restrictions between both countries. (file photo)

"Certainly that's started with Singapore, and we do have frequent contact with Australia, and at officials' level I couldn't tell you how far along those have got. But they will be a part of my ongoing agenda with PM [Prime Minister] Morrison," Ardern said.

"As I've said, though, I think both of us have the same goal in mind at the moment: get it under control in our own countries, and then we can talk about together what we're able to achieve."

Both New Zealand and Australia have put in place strict border controls to limit the spread of Covid-19, permitting only citizens or permanent residents into the country if they undertake a 14-day quarantine.

New Zealand citizens who "usually reside in Australia" are also able to cross the border.

Both Australia and Singapore are among countries, including New Zealand, which are considered to have better managed the Covid-19 pandemic than others.