Former Trump campaign chairman Paul Manafort shared polling data and discussed U.S. policy in Ukraine with a Russian national with alleged ties to that country’s intelligence agencies, according to a Tuesday court filing that was meant to be redacted by Manafort’s lawyers but mistakenly was made public.

On “more than one occasion,” Manafort shared polling data related to the 2016 presidential campaign and discussed a Ukrainian peace plan with Konstantin Kilimnik, a former business associate, according to the filing by Manafort’s legal team.

Manafort and Mr. Kilimnik also met in Madrid, according to the filing. The lawyers did not disclose when the meeting took place, but an unredacted portion of the filing said some events occurred while Manafort was managing President Trump’s 2016 campaign.

The details are the first public revelation linking a Trump campaign official to someone believed to have ties to the Kremlin. It is the also the first acknowledgment that special counsel Robert Mueller, who is investigating Russian meddling in the 2016 election, may have found a connection between the Trump campaign and Russia.

Mr. Kilimnik is believed to a key figure in the Mueller probe. He has not been charged with any crime related to election interference, but he does face charges for allegedly helping Manafort tamper with witnesses before his criminal trial in the District of Columbia.

The revelations were supposed to be redacted but could be accessed because of an apparent filing error. The error later was corrected.

The filing was a response by Manafort’s attorneys to Mr. Mueller’s accusation that he had lied to prosecutors. After pleading guilty in a D.C. federal court last year, Manafort agreed to cooperate with Mr. Mueller. However, Mr. Mueller said Manafort had provided untrue information and threatened to void his plea agreement.

Manafort’s attorneys insisted he “provided complete and truthful information to the best of his ability.”

“He attempted to live up the requirements of his cooperation agreement and provided meaningful cooperation relating to several key areas under current government investigation,” Manafort attorney Kevin Downing wrote.

If Manafort forgot details, Mr. Downing said, it was because his time in a Virginia jail had taken a toll on his physical and mental health.

“For several months Mr. Manafort has suffered from severe gout, at times confining him to a wheelchair,” the attorney wrote. “He also suffers from depression and anxiety and, due to the facility’s visitation regulations, has had very little contact with his family.”

Mr. Downing also chalked up Manafort’s confusion to the hours and lengths of his interviews, which spanned nine meetings with Mr. Mueller’s team. The attorney said Manafort began talking with investigators before dawn, answering questions for “many hours” and “usually the entire day.”

Although Manafort’s attorneys could request an evidentiary hearing on the claim he lied to Mr. Mueller’s team, they suggested the matter be addressed in a pre-sentencing report compiled by the probation office.

However, U.S. District Judge Amy Berman Jackson could hold such a hearing if she finds it necessary.

Mr. Mueller’s team said last month Manafort lied about his connection with Mr. Kilimnik and a wire transfer to a company he was working with.

But his attorneys on Tuesday chalked up the discrepancies to “confusion” on Manafort’s part. They said Manafort was unclear on how the payment was recorded by his accountant. His lawyers also said prosecutors have not provided witness statements disputing Manafort’s account.