People linked to the Trump administration and Congress attempted to obstruct former National Security Adviser Michael Flynn’s efforts to cooperate with special counsel Robert Mueller’s probe, according to court documents unsealed Thursday.

The filing in a Washington, D.C., federal court says Flynn informed the special counsel of “multiple instances” both before and after his guilty plea where either he or his attorneys received communications “from persons connected to the administration or Congress.”

Federal prosecutors say those communications could have affected both Flynn’s “willingness to cooperate and the completeness of that cooperation.”

“The defendant even provided a voicemail recording on such communication,” Mr. Mueller wrote in the filing. “In some of those instances, the [special counsel] was unaware of the outreach until being alerted to it by the defendant.”

No other details were provided in the documents, which were filed in December as a redacted portion of Flynn’s sentencing memorandum.

The court filing doesn’t say who left the voicemail, but the Mueller report said President Trump’s personal lawyer left Flynn a message in November 2017 addressing his cooperation with the government.

“It wouldn’t surprise me if you’ve gone on to make a deal with … the government,” the unidentified attorney said in the voicemail message, according to Mr. Mueller.

If “there’s information that implicates the president, then we’ve got a national security issue … so, you know … we need some kind of heads up. Um, just for the sake of protecting all our interests if we can. … Remember what we’ve always said about the president and his feelings toward Flynn and, that still remains,” the Mueller report said.

In a separate court filing, Judge Emmet Sullivan ordered prosecutors to turn over redacted portions of Mr. Mueller’s report, which would make them public. Under the order, prosecutors would have to hand over a transcript of the voice message detailed in the Mueller report along with other transcripts, including Flynn’s talks with Russian officials.

Rep. David Cicilline, Rhode Island Democrat, renewed calls for Mr. Trump’s impeachment based on the court filing, calling the newly revealed information “disturbing.”

“Combined with the damning revelations in the Mueller report and the president’s ongoing efforts to obstruct Congress, it’s evident that this president has no regard for the law,” said Mr. Cicilline, a member of the House Judiciary Committee.

“Opening an inquiry on impeachment isn’t just on the table, it’s looking more and more like this may be the only way to hold this president accountable for his wrongdoing,” he continued.

Flynn pleaded guilty in December 2017 to lying to investigators about his conversations with Russian Ambassador Sergey Kislyak just before President Trump was inaugurated. He faces up to six months in jail, although a sentencing date hasn’t been set.

Mr. Mueller’s team had previously told the court that Flynn should receive little or no jail time because he provided “substantial assistance” to their investigation into Russian election meddling.

The filing unsealed Thursday offered a few more details about Flynn’s cooperation.

Prosecutors say he provided information about discussions within Mr. Trump’s campaign to reach out to WikiLeaks. Just before the 2016 election, WikiLeaks released emails hacked from the Democratic National Committee and Hillary Clinton’s campaign.

Flynn also cooperated in the case against his business associate Bijan Kian, according to the filing.

Mr. Kian was charged in December with failing to register as a foreign agent. He has pleaded not guilty and a trial is slated for July. Flynn is expected to testify during the trial.

Flynn also appears to have cooperated with Mr. Mueller’s team on another investigation, but details are entirely redacted.

Mr. Mueller wrapped up his investigation in March, but declined to make a call on whether Mr. Trump obstructed justice. Attorney General William P. Barr and then-Deputy Attorney General Rod Rosenstein said there wasn’t enough evidence to pursue the issue.