WASHINGTON — Special counsel Robert Mueller disclosed more details Tuesday of former national security adviser Michael Flynn’s efforts to cover up the extent of his ties to the government of Turkey while he was a top official on President Donald Trump’s campaign and transition.

The documents specifically state that a key component of Flynn’s work for Turkey involved the government’s efforts to remove from the U.S. a Turkish cleric living in Pennsylvania. Turkish President Recep Tayyip Erdogan accuses the cleric, Fethullah Gulen, of orchestrating a failed coup against him in July 2016. Flynn began working for Turkey about a month later.

Federal prosecutors said in the court filing, which refers to Gulen, though not by name, that Flynn’s decision not to disclose that he was aiding the Turkish government "impeded the ability of the public to learn about the Republic of Turkey's efforts to influence public opinion about the failed coup, including its efforts to effectuate the removal of a person legally residing in the United States."

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Flynn’s false statements about his connections to Turkey were included in his plea agreement with Mueller announced in December 2017, but that document described the project simply as focused on U.S. companies’ confidence in doing business in Turkey.

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Tuesday's filing, while more detailed, did not touch on some of the other possible ties between Flynn and Turkey that Mueller’s team has looked into, leaving it unclear what, if anything, further may be disclosed at a later time. NBC News reported, for instance, that Mueller’s team was looking into whether Flynn met with senior Turkish officials in December 2016 about a possible deal under which Flynn would be paid to orchestrate the return of Gulen to Turkey once in the White House.

Since the failed coup, Turkey has repeatedly demanded the U.S. extradite Gulen. The Trump White House recently asked federal law enforcement agencies to look into legal ways to remove the cleric from the U.S. in attempt to ease Erdogan’s anger after the Saudi government’s murder of Jamal Khashoggi at the Saudi consulate in Istanbul.

Flynn did not register with the U.S. government for his 2016 work for Turkey, as is required by law, until almost a month after he was fired as Trump’s national security adviser in February 2017. Tuesday’s court filing confirms that Flynn and his company were paid $530,000 for the work, which ended after Trump won the election in November.

Prosecutors further state that Flynn’s role as "a national security advisor and surrogate for the Trump campaign who opined publicly on foreign policy and national security issues" made his work for Turkey critical to disclose.

"The defendant’s business relationship with the Republic of Turkey was thus exactly the type of information FARA was designed to ensure was within the public sphere," the documents filed Tuesday said.

The filing also cited Flynn’s false statement that he had written an op-ed on Election Day that was favorable to Erdogan’s view of Gulen "at his own initiative."

"The cleric’s responsibility for the coup attempt was a subject of great debate, and the defendant’s op-ed about the cleric’s role was valuable to the Republic of Turkey’s efforts to shape public opinion," prosecutors wrote. Flynn’s decision not to disclose Turkey’s role in the op-ed "again deprived the public of the very transparency FARA was designed to ensure."

CORRECTION (Dec. 5, 2018, 8:30 am ET): An earlier version of this article misstated the date on which federal prosecutors filed the sentencing memo. It was filed on Tuesday, not Thursday.