US President Donald Trump is working on the extradition of a US-based Muslim cleric accused of orchestrating a failed military coup in 2016, Turkey's foreign minister said on Sunday.

"In Argentina, Trump told Erdogan they were working on extraditing [Fethullah] Gulen and other people," Turkish Foreign Minister Mevlut Cavusoglu said, referring to the G20 meeting last month where the US and Turkish leaders met.

Turkey has long-sought the extradition of Mr Gulen, who was formerly an ally of Turkish President Tayyip Erdogan and seeks to dismantle his support network.

"I have recently seen a credible probe by the FBI on how the Gulen organisation avoids taxes," Mr Cavusoglu told a conference in Doha.

Mr Gulen has lived in self-imposed exile in the United States for nearly two decades but was accused of orchestrating a failed military coup which saw tanks and helicopters attack the Turkish parliament and shoot unarmed civilians.

Mr Gulen denies involvement in the failed coup. Turkey accuses Mr Gulen of running a counter-state from afar, and Mr Erdogan said last week they would start new initiatives to target the financing of Mr Gulen's supporters.

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In October, Mr Gulen's brother was jailed for 10 and-a-half years for being a member of his brother's group, which the Turkish state say is a terror organisation. He had been held without conviction for two years on the charges.

In the years following the coup, thousands of alleged Gulenists in the military, police, judiciary and civil service were dismissed and detained.

Extradition of Mr Gulen would require approval by the US Congress, majority control of which Mr Trump will lose in January. But even within his own party, Mr Trump might struggle for support for the move.

Turkey recently released a US pastor who was arrested on terrorism charges following a long spell of diplomacy between the two countries, and in the midst of the fall out of the killing of dissident journalist Jamal Khashoggi.