The letter was dated Monday, the same day that Mr. Trump praised Mr. Stone on Twitter for having the “guts” to stand up to Mr. Mueller. Mr. Stone’s lawyer said that the letter was sent before Mr. Trump’s tweet.

A grand jury in Washington has been investigating whether Mr. Stone had any advance knowledge of how WikiLeaks planned to use documents stolen from Democratic computers by Russian agents during the 2016 presidential campaign.

Prosecutors said Mr. Flynn’s more than 33 years of military service — he was a three-star Army general before being fired as the head of the Defense Intelligence Agency in 2014 — should be taken into account when Judge Emmet G. Sullivan of the United States District Court for the District of Columbia sentences him on Dec. 18. But they also noted he should have known better than to lie to the F.B.I. “Senior government leaders should be held to the highest standards,” they wrote.

Close observers of Mr. Mueller’s investigation had hoped his team might provide revealing details about possible cooperation between Trump associates and Russia, but in typical fashion, the special counsel’s office kept its cards closely held.

Though the lack of details suggested that Mr. Mueller’s investigation remains active, one of the president’s personal lawyers, Rudolph W. Giuliani, seized on it to underscore that Mr. Mueller had yet to prove any Trump associates conspired with Russia’s campaign of disruption. “This is what we get for $30 million and two years of an investigation and no evidence of collusion, and we get a process charge?” he said, referring to Mr. Flynn’s plea of lying to the F.B.I. and rounding up the estimated costs of the special counsel inquiry.

Mr. Flynn, who gained notoriety after he left the military for his view of Islamic terrorism as an existential threat to the United States, began advising the Trump campaign in early 2016. About a week after his surprise election victory, Mr. Trump named Mr. Flynn as his future national security adviser.

During the presidential transition, Mr. Flynn discussed with Mr. Kislyak a coming United Nations Security Council vote on whether to condemn Israel’s building of settlements. At the time, the Obama administration was preparing to allow a Security Council vote on the matter.