Anthony Albanese is considering Donald Trump’s invitation for Australia to join the US president’s proposed “board of peace” initiative, despite concerns its could undermine the work of existing organisations including the UN.

The prime minister confirmed Australia had been invited to join the new international body at the weekend, promising serious consideration, especially around proposals to advance Middle East peace efforts.

The leaders of France, Germany, Italy, Hungary, Canada, Argentina, the European Commission and Middle East powers have been invited to join the new US-led organisation, which promises to be a “more nimble and effective international peace-building body”.

A draft charter shows Trump will serve as chair, with national leaders expected to make up its top tier of members. Countries are expected to serve three-year terms, with those paying US$1bn to the US expected to be given permanent status.

“We’ve received correspondence from the president, that arrived, I think, last night,” Albanese said on Monday.

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“That’s something we haven’t had time to consider. We’ll consider all of these approaches respectfully and through our proper processes.”

The board was originally envisaged as part of Trump’s plans for the reconstruction of Gaza, much of which was destroyed during Israel’s war against terror group Hamas.

A so-called “Gaza executive board” is expected to operate under the broader board of peace.

International media reported the charter described the board’s mandate as promoting stability and governance around the world, while seeking “enduring peace in areas affected or threatened by conflict”.

Such work is usually the remit of the UN.

Diplomats around the world have expressed concerns Trump has been trying to undermine the UN. Asked about the board for peace, a spokesperson for the UN secretary general, Antonio Guterres, told Reuters that Guterres “believes member states are free to associate in different groups”.

Trump has been a regular critic of the UN and other multilateral organisations. He has even canvassed withdrawing the US from the 193-member international body. Earlier this month he withdrew the US from more than 30 UN subsidiary organisations, calling participation “contrary to US national interests”.

UN officials say the US, which is required to pay 22% of the UN’s regular budget, owes $1.5bn, according to Reuters.

Albanese previously used an interview with Kiis FM to talk up his relationship with Trump, after his successful visit to Washington in October.

“I deal with people respectfully. And where there’s area of disagreement, sometimes you just got to put them aside and work on what you agree on and your common interest.”

Trump has appointed the US secretary of state, Marco Rubio, and former British prime minister Tony Blair to the newly-created board. Albanese is a friend of Blair and the pair last met in London in September.

The shadow foreign affairs minister, Michaelia Cash, told Guardian Australia that she believed Labor should carefully consider Trump’s proposal.

“The Coalition looks forward to understanding more about the objectives, structure, membership and implications of this proposal before Australia commits to any engagement,” she said.

“It is important for all nations to work together to rebuild Gaza and ensure that it is no longer under the control of the Hamas terrorists.”

But the Greens’ defence spokesperson, David Shoebridge, condemned Trump’s initiative.

“Trump is trying to sell Palestinian sovereignty for US$1bn per seat while Palestinians are still being bombed and starved under the so-called ‘ceasefire’.

“This isn’t diplomacy, it’s profiteering off genocide. Australia better not touch this with a 10-foot pole,” he wrote on social media.

The government has pushed back on Trump’s plans to impose trade tariffs on countries opposing his ambitions to control Greenland, calling for the autonomous Danish territory to decide its own future.

The defence minister, Richard Marles, sidestepped questions about what the US taking control of Greenland would mean for Australian foreign policy on Monday, even as European Union and Nato members warned against the plan.

“Nato has played a very important role and continues to be very strong,” Marles said.

“We completely agree with the fact that the future of Greenland has to be a matter for Denmark and Greenland. They are the sovereign powers here, and that’s what Australia recognises and that’s how we see this issue.”

The finance minister, Katy Gallagher, said on Sunday that Trump’s threats of tariffs of as high as 25% on Denmark, Norway, Sweden, France, Germany, the UK, the Netherlands and Finland were the wrong course.

She declined to comment on the potential ramifications for Australia’s foreign and defence policy if Trump sought to take territory from a Nato member.