WASHINGTON — Of the few hints to emerge from the special counsel, Robert S. Mueller III, about evidence of possible collusion between President Trump’s campaign and Russia, one of the most tantalizing surfaced almost in passing in a Washington courtroom last week.

Comments by one of Mr. Mueller’s lead prosecutors, disclosed in a transcript of a closed-door hearing, suggest that the special counsel continues to pursue at least one theory: that starting while Russia was taking steps to bolster Mr. Trump’s candidacy, people in his orbit were discussing deals to end a dispute over Russia’s incursions into Ukraine and possibly give Moscow relief from economic sanctions imposed by the United States and its allies.

The theory was offered almost as an aside by the prosecutor, Andrew Weissmann, during a discussion of contacts between Mr. Trump’s former campaign chairman, Paul Manafort, and a longtime Russian associate, Konstantin V. Kilimnik, whom investigators have linked to Russian intelligence.

A closer look at the transcript, released late Thursday, shows that the prosecutors have been keenly focused on discussions the two men had about a plan to end the conflict that followed Russia’s invasion of Ukraine and annexation of Crimea in 2014. Persuading the United States to ease or end the American-led sanctions imposed to punish Moscow for its aggression has been a primary goal of Russian foreign policy.

According to the transcript, which was heavily redacted, Mr. Manafort and Mr. Kilimnik repeatedly communicated about a so-called peace plan for Ukraine starting in early August 2016, while Mr. Manafort was still running Mr. Trump’s campaign, and continuing into 2018, months after Mr. Manafort had been charged by the special counsel’s office with a litany of crimes related to his work in the country. The prosecutors claim that Mr. Manafort misled them about those talks and other interactions with Mr. Kilimnik.

Pressed by the judge at Monday’s hearing to say why Mr. Manafort’s alleged lies mattered, Mr. Weissmann gave a broad hint about the thrust of the investigation.

“This goes to the larger view of what we think is going on, and what we think is the motive here,” Mr. Weissmann said. “This goes, I think, very much to the heart of what the special counsel’s office is investigating.”

Mr. Weissmann did not elaborate. The hearing’s purpose was narrow — determining whether Mr. Manafort had breached his plea agreement by misleading the prosecutors about Mr. Kilimnik and other matters. Mr. Kilimnik was charged last June with conspiring with Mr. Manafort to obstruct justice by trying to shape the accounts of prospective witnesses in Mr. Manafort’s case.

Yet Mr. Weissmann’s cryptic comments suggest that the special counsel’s investigation — which Mr. Trump has sought to dismiss as a witch hunt and which the acting attorney general, Matthew G. Whitaker, has said will wrap up soon — is still pursuing the central question of whether there was some kind of deal between Russia and the Trump campaign.