The filing could give new ammunition to Mr. Manafort’s defense team, which has argued that prosecutors overreached in accusing Mr. Manafort of lying because they were too eager to believe Mr. Gates. Lawyers for Mr. Manafort have repeatedly contended that Mr. Gates, who has been cooperating with Mr. Mueller’s team for the past year, is not a credible witness. Mr. Gates pleaded guilty to lying to federal investigators and conspiracy and is assisting the special counsel in hopes of a lighter sentence.

The subject in dispute was unclear from the filing, but one issue that prosecutors have said that Mr. Manafort lied about was whether he ordered Mr. Gates to give Trump campaign polling data to Mr. Kilimnik before the election. Court records suggest that prosecutors relied heavily on Mr. Gates for evidence of data transfers.

Mr. Manafort pleaded guilty last September to two conspiracy counts and, like a number of former Trump aides, agreed to cooperate with the special counsel’s investigation. But after a lengthy closed hearing on Feb. 13, Judge Jackson agreed with prosecutors that Mr. Manafort had breached his plea agreement by lying to them about three matters, including his relationship with Mr. Kilimnik.

That ruling could influence the severity of the punishment Mr. Manafort receives as a result of two prosecutions by the special counsel’s office. He is scheduled to be sentenced on March 7 by Judge T.S. Ellis III of United States District Court in Northern Virginia for eight counts involving financial fraud. Judge Jackson will sentence him for the two conspiracy crimes six days later. The combined sentences could mean that Mr. Manafort, 69, spends the rest of his life in prison.

Like other court filings discussing Mr. Manafort’s interactions with Mr. Kilimnik, the latest one, filed before Judge Jackson, was heavily redacted to protect active federal investigations. Even so, it makes clear that the prosecutors were trying to defend Mr. Gates’s credibility while at the same time correcting the record on which Judge Jackson relied in determining that Mr. Manafort had lied to them.