Former US National Security Advisor General Michael Flynn arrives for his sentencing hearing at US District Court in Washington, DC on December 18, 2018. Saul Loeb / AFP/Getty Images

Washington -- Former White House national security adviser Michael Flynn told the special counsel's office that people connected to the Trump administration and Congress sought to influence his cooperation with the Russia investigation, and he provided a voicemail recording of one such communication, prosecutors said in a court filing made public Thursday.

Meanwhile, the judge in the case ordered that portions of special counsel Robert Mueller's report that relate to Flynn be unredacted and made public by the end of the month. CBS News justice correspondent Paula Reid says it will give the public its first look at some of the redacted portions from Mueller's Russia report.

Thursday's order from U.S. District Judge Emmet Sullivan is the first time a judge is known to have directed the Justice Department to make public any portion of the report that the agency had kept secret. It could set up a conflict with Attorney General William Barr, whose team spent weeks blacking out from the report grand jury information, details of ongoing investigations and other sensitive information.

Prosecutors revealed details about Flynn's communications in a court filing aimed at showing the extent of his cooperation with Mueller's investigation into ties between the Trump campaign and Russia. Flynn, a vital witness in the probe, is awaiting sentencing after pleading guilty to lying to the FBI about his contacts during the presidential transition period in 2016 with the-then Russian ambassador to the United States.

Prosecutors did not identify the people with whom Flynn was in touch nor did they describe the exact conversations.

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But they said Flynn recounted multiple instances in which "he or his attorneys received communications from persons connected to the Administration or Congress that could have affected both his willingness to cooperate and the completeness of that cooperation." Prosecutors say they were unaware of some of those instances, which took place before and after his guilty plea, until Flynn told them about them.

Mueller's report did not reach a conclusion on whether Mr. Trump illegally obstructed justice, but he did examine nearly a dozen episodes for potential obstruction, including efforts by the president to discourage cooperation.

The report reveals that after Flynn began cooperating with the government, an unidentified Trump lawyer left a message with Flynn's attorneys reminding them that the president still had warm feelings for Flynn and asking for a "heads-up" if Flynn knew damaging information about the president.

Sullivan ordered prosecutors Thursday to give him a copy of the audio recording they reference in the court filing, and to make public a transcript of that call. He also directed them to file publicly transcripts of any calls with Russian officials such as the ambassador, Sergey Kislyak.

CBS News' Reid said the transcripts of any calls between Flynn and Russian officials will be made public by May 31.

Flynn was supposed to have been sentenced in December, with prosecutors saying he was so cooperative and helpful in their investigation that he was entitled to avoid prison. But after a judge sharply criticized Flynn during his sentencing hearing, Flynn asked for it to be postponed so that he could continue cooperating with prosecutors and reduce the likelihood of being sent to prison.

The document also details how Flynn assisted investigators as they looked into whether the Trump campaign conspired with the Kremlin to sway the outcome of the 2016 election.

Flynn described to investigators statements from senior campaign officials in 2016 about WikiLeaks - which received and published Democratic emails that were hacked by Russian intelligence officers "to which only a select few people were privy," prosecutors said. That includes conversations with senior campaign officials "during which the prospect of reaching out to WikiLeaks was discussed."

A redacted version of Mueller's report released last month said that the evidence did not establish a criminal conspiracy between Russia and the campaign.