British billionaire Richard Branson weighed in on the political impasse gripping the Maldives on Friday with an open letter to the new president urging him to hold fair and free elections.

The founder of the Virgin brand said he was astounded that President Mohamed Waheed was involved in the fall of his predecessor, Mohamed Nasheed, who claims he was forced to resign in a military coup backed by Islamic extremists.

In the letter to Waheed posted on his personal blog, Branson recalled the "real pleasure" of meeting the then vice president and his "delightful wife" when he was in the Maldives in October for a meeting on global warming.

"You personally said to me that the Maldives needed a truth and reconciliation commission to examine the past misdeeds and the people who perpetuated them, and asked if I would speak with The Elders to see whether they would set one up," he wrote.

"Therefore, forgive me for finding it completely astounding that you have been part of an overthrow of a democratically elected government that has effectively let the old regime back into power."

He said he hoped that Waheed had been given no choice but to take part in the transfer of power, which he said was "dreadful".

"As interim president, you are in a position to do the right thing. We beg you to make sure that there are fair and free elections held this year, as the Commonwealth Ministerial Action Group have called for," he said.

The action group, which deals with serious violations of the Commonwealth's political values, on Wednesday urged the Maldives to hold elections this year but stopped short of suspending the archipelago's membership.