New Zealand would back plans to remove Andrew Mountbatten-Windsor from the line of royal succession, a spokesperson for Prime Minister Christopher Luxon has said.

"If the UK Government proposes to remove Andrew Mountbatten-Windsor from the order of succession, New Zealand would support it," the spokesperson said in a statement.

It comes a day after Australian Prime Minister Anthony Albanese said that his government "would agree to any proposal" to remove Andrew from the line of succession over his ties to to paedophile financier Jeffrey Epstein.

Andrew was arrested on suspicion of misconduct in public office on Thursday. He has consistently and strenuously denied any wrongdoing.

The UK government is considering introducing legislation to remove Andrew from the line of succession.

In a press conference on Tuesday in Auckland, the prime minister said his government had been in contact with the UK Cabinet Office over the last week - and that his views had been made clear before the letter from Anthony Albanese was published.

"Our Cabinet Office talks to their Cabinet Office and we have conversations all the time... our position is well understood and I'm telling you what our position is now," Luxon said.

He continued: "The bottom line is no one is above the law and once that investigation is closed, should the UK government decide to remove him from the line of succession, that is something we would support."

Earlier on Tuesday, New Zealand's deputy Prime Minister David Seymour said he did not think the issue was a high priority for people in the country.

"I think we've got 99 problems most New Zealanders are facing right now," he told RNZ.

"So, of all of the things that you could ask me about or we could be worried about right now, that's probably a wee way down the list."

Speaking after his brother Andrew's arrest, King Charles had said: "What now follows is the full, fair and proper process by which this issue is investigated in the appropriate manner and by the appropriate authorities."

In a letter made public yesterday, the Australian prime minister wrote that he was in agreement with His Majesty, and "the law must now take its full course".

"These are grave allegations and Australians take them seriously," read the letter, which was addressed to Sir Keir Starmer.

A spokesman for the UK prime minister confirmed the letter from Albanese had been received and said the government was "considering whether further steps are required in relation to Andrew Mountbatten-Windsor".

"Given the ongoing police investigation it would not be appropriate for the government to comment further at this stage," the spokesman added.

Darren Jones, chief secretary to the UK prime minister, told MPs on Monday that the government was "not ruling out action in respect of the line of succession at this stage", following the arrest of the Andrew on suspicion of misconduct in public office on Thursday.

He remains eighth in line to the throne despite being stripped of his titles, including "prince", in October.

Removing the former prince from the line of succession would require an act of Parliament supported by the 14 Commonwealth countries where King Charles III, his brother, is head of state, including Australia and New Zealand.

The last time someone was removed from the line of succession by an act of Parliament was in 1936, when the former Edward VIII and his descendants were removed due to his abdication.

Buckingham Palace has not publicly commented on the government's consideration of legislation to remove Andrew from the line of succession.