Prime Minister Jacinda Ardern has arrived in Melbourne for a packed five-day schedule after her trip to Europe, saying it was "excellent" to get her business mission under way at last.

Ardern was welcomed with a ceremony by Wurundjeri elder, Aunty Joy Wandin-Murphy, at the Melbourne Cricket Ground today.

Afterward, she told media the trip had been long-planned. Ardern had intended to visit Australia with a delegation in 2021 but that was scrapped after the spread of the Delta variant closed the travel bubble.

"We've had this trade mission in the planning for quite some time and it's excellent to now be here.

"In my mind, regardless of Covid this is the kind of trade mission I would be keen to lead. This is one of our key markets, whether it's trade, tourism or investment."

She said one of the things her visit to Europe had shown her was that reopening after Covid-19 was not necessarily a smooth process.

"[There are] very challenging circumstances in some of those big hubs in Europe, and in New Zealand there's been a relatively smooth reopening when it comes to our borders."

Australia has just dropped its requirement for travellers into the country to have to show a vaccination certificate. Ardern said while unvaccinated New Zealand citizens and permanent residents could already come in, it was not planning to drop the requirement for other travellers, such as tourists or business travellers, yet.

"But we always said we will keep an eye on our border restrictions and make sure they are fit for purpose."

She said most people were vaccinated, so it was not a barrier for entry for many.

Ardern's visit will be a mix of business and politics - including a chance to follow up with Australia's Prime Minister Anthony Albanese on his promise to consider the way the deportations policy was applied.

On the 501s issue, Ardern said she had not set an expectation to resolve the issue straight away while on the trip. Underpinning that issue was the path to citizenship for New Zealanders, she said.

None of the issues could be resolved in weeks and changes the Government was after would take a bit of time, Ardern said.

Ardern said she also expected to discuss the topic of inflation while in Australia. There was a common experience and common approach to dealing with it, she said.

The PM's visit to Melbourne and Sydney with several ministers and a business delegation will be a mix of business and tourism events, and political meetings.

It will end on Friday with the Australia-New Zealand Leadership Forum in Sydney – the first time the Forum has taken place in person since Covid-19 closed borders.

Ardern and Australia's PM Anthony Albanese will both speak at that. It will also be attended by ministers Damien O'Connor (trade and export growth), Stuart Nash (tourism and small business), Willie Jackson (Māori development), Michael Wood (immigration), Ayesha Verrall (Covid-19 response), James Shaw (climate change) and Grant Robertson (finance) – provided he has recovered from Covid-19.

That meeting will be a chance for a formal catch-up between Ardern and Albanese after the two leaders held preliminary talks about a month ago, soon after Albanese won the Australian election.

Ardern is expected to ask for any further thoughts Albanese has had about policies such as Australia's deportations programme and the pathway to citizenship for New Zealanders living in Australia. They are also likely to discuss the topics that will dominate at next week's Pacific Islands Forum, where the Pacific leaders are expected to discuss issues including the Solomon Islands' recent agreement with China.

Ardern arrived in Australia earlier today with a bag full of gains from her week in Europe. Those gains included the long-negotiated New Zealand - European Union Free Trade Agreement after a last minute push by Ardern and negotiators.

She finished that trip in London and a meeting with British PM Boris Johnson - and more generous terms for a visa allowing younger New Zealanders to live and work in the United Kingdom. She also had a private meeting with Prince William.

While in Australia, Ardern is also scheduled to meet Victoria Premier Daniel Andrews and NSW Premier Dominic Perrotet, and deliver a foreign policy speech at the Lowy Institute.

A major tourism summit, including New Zealand and Australian ministers and the chief executives of tourism companies is also scheduled as both countries seek to woo back the tourist trade.

It is the start of a three-week recess for MPs in New Zealand. Acting Prime Minister Grant Robertson has Covid-19 but was hoping to recover in time to travel over later in the week for the ANZLF talks.

Covid-19 has also caught up with Foreign Affairs Minister Nanaia Mahuta, who was due to travel to Fiji for the Pacific Islands foreign ministers' meeting later this week, ahead of next week's leaders' meetings. The Government will send another minister instead.