Australia PM backs removing UK's Andrew from line of succession
In a letter to UK counterpart Keir Starmer, Albanese said: "My Government would agree to any proposal to remove him from the line of royal succession".
"These are grave allegations and Australians take them seriously," Albanese added.
Starmer's official spokesman confirmed the UK government had received Albanese's letter.
"We're considering whether further steps are required in relation to Andrew Mountbatten-Windsor and we're not ruling anything out, but given the ongoing police investigation, it wouldn't be appropriate for the government to comment further at this stage," he told reporters.
The former prince was arrested on Thursday on suspicion of misconduct in public office for allegedly sharing sensitive information with the late US sex offender Epstein while serving as the UK's trade envoy.
In the face of a torrent of often tawdry revelations about the two men's ties, King Charles III stripped his younger brother of all his titles in October and ordered him to leave his home in Windsor.
Further revelations about the depth of Andrew's friendship with the American financier emerged when the US Justice Department released a new tranche of millions of Epstein documents last month.
But the son of the late queen Elizabeth II remains eighth in line to the British throne after Princess Lilibet, the daughter of his nephew, Prince Harry.
The British government is mulling passing a law to remove Andrew from the line of succession but said they would wait until the police complete their inquiries.
Officials say that any such legislation would also require the agreement of the 14 other Commonwealth countries where the king remains the head of state.
"It's right that the police investigation should take its course. That has primacy here," Starmer's spokesman added.
Charles on Thursday issued a rare, personally signed statement insisting "the law must take its course".
Albanese, who favours changing his country to a republic, told Starmer on Monday he agreed with the king.
"The law must now take its full course and there must be a full, fair and proper investigation," he wrote.
Australia was a British colony for more than 100 years and gained de facto independence in 1901, but has never become a fully fledged republic.
In a 1999 referendum, Australians narrowly voted against removing then queen Elizabeth as head of state.