The prosecutors convinced Judge Jackson that Mr. Manafort had deceived them about his talks with Mr. Kilimnik, including their conversations about a possible deal that might have served the Kremlin’s ends. The two men repeatedly discussed a proposal to resolve a conflict over Russia’s incursions into Ukraine, possibly giving Moscow relief from punishing American-led sanctions that had been imposed after Russia seized Ukraine’s Crimean Peninsula.

Andrew Weissmann, one of Mr. Mueller’s top deputies, told the judge this month that the interactions between the two men go “to the larger view of what we think is going on and what we think is the motive here.” He suggested that Mr. Manafort had misled the prosecutors into believing that he had rejected the Ukraine plan with Mr. Kilimnik out of hand during a meeting on Aug. 2, 2016, while Mr. Manafort was still running Mr. Trump’s campaign. Only after he was confronted with evidence did Mr. Manafort acknowledge that he and Mr. Kilimnik continued to discuss the proposal on at least three other occasions after Mr. Trump was elected, he said.

The prosecutors also told the judge that Mr. Manafort deceived them about transferring Trump campaign polling data to Mr. Kilimnik during the campaign. The New York Times has reported that the data included both private and public data, and that Mr. Manafort wanted the information delivered to two Ukrainian oligarchs who had financed Ukrainian political parties that were aligned with Russia.

Mr. Manafort’s lawyers had suggested that Mr. Manafort had only wanted to share public data in the interest of promoting himself and maybe winning lucrative work overseas. The oligarchs and their allies had paid Mr. Manafort tens of millions of dollars in Ukraine to help Viktor F. Yanukovych win the presidency there. Mr. Yanukovych was forced out of power in a popular uprising in 2014 and fled to Russia.

But the prosecutors seem to have pitted Mr. Manafort’s assertions against those of Rick Gates, Mr. Trump’s former deputy campaign chairman. Mr. Gates pleaded guilty to two felonies and has been cooperating with Mr. Mueller’s team for the past year.

During the earlier hearing, Mr. Weissmann appeared to suggest that Mr. Manafort’s lies about the polling data were too important to dismiss as innocent memory lapses. Whether any Americans, wittingly or unwittingly, engaged with Russians who were trying to interfere in the presidential election went to “the core” of the special counsel’s inquiry, Mr. Weissmann said.

He suggested that Mr. Manafort might have been trying to cover up the data transfer because it might hurt his chances of winning a presidential pardon for his crimes.

If it became known that Mr. Manafort had given Mr. Kilimnik the campaign’s polling data, Mr. Weissmann said, it could have “negative consequences in terms of the other motive that Mr. Manafort could have, which is to at least augment his chances for a pardon.”