Washington (CNN) While he was cooperating with special counsel Robert Mueller's investigation, former Trump national security adviser Michael Flynn contacted at least one member of Congress who was publicly criticizing the special counsel probe, according to messages obtained by CNN.

Flynn sent Twitter direct messages to Rep. Matt Gaetz, encouraging the Florida Republican to "keep the pressure on." It's not clear if Flynn sent additional messages to other lawmakers.

"You stay on top of what you're doing. Your leadership is so vital for our country now. Keep the pressure on," Flynn wrote in an April 2018 message to Gaetz, which was obtained by CNN.

On the evening Flynn sent the message to Gaetz, the lawmaker had appeared on Fox Business' "Lou Dobbs Tonight," where he criticized the Mueller investigation.

"We've got to play a far stronger role in exposing the hypocrisy at the Department of Justice," Gaetz said in the April 3, 2018, appearance. "With no evidence of collusion, with no evidence of any crime whatsoever, they unleashed Bob Mueller to go investigate things that happened before Donald Trump was even contemplating running for president."

That same hour, Flynn sent Gaetz the direct message.

Gaetz also received a message in February of this year. On the day that Attorney General William Barr was confirmed, Flynn sent Gaetz GIFs of a bald eagle and an American flag, without any accompanying text.

Gaetz, who called for Mueller's resignation and has been among the most vocal critics of the special counsel, confirmed that he received the messages, but said he did not respond. Gaetz did not have a prior relationship with Flynn, he said.

The messages raise fresh questions about Flynn's contact with politically powerful people following his guilty plea in the Mueller probe. They add to a perception that has played out in Flynn's courtroom proceedings that he has modulated between helping the special counsel and stoking Mueller's critics in the Republican Party.

Flynn's cooperation with Mueller is in the spotlight again after court records unsealed on Thursday revealed that Flynn had told the special counsel that "persons connected to the administration or Congress" had contacted him -- with an attorney for President Donald Trump even leaving a voicemail -- and potentially attempted to influence his willingness to cooperate. Mueller credited Flynn with telling investigators he had been contacted, and the special counsel asked a judge last year to consider not sending Flynn to jail for his crime because he had been so helpful.

Flynn's disclosures to Mueller raised the possibility that Trump or others around the President may have attempted to obstruct justice with the outreach to Flynn. But Mueller did not go into detail on that possibility in either the new Flynn court filing or in his final report on possible obstruction of justice.

Instead, Mueller said he could not determine if Trump had directed his personal attorney to leave a voicemail for Flynn's attorney about him cutting a plea deal.

Flynn's attorney declined to comment on Friday.

Gaetz attacked Mueller

Flynn has been almost completely silent in public since he pleaded guilty in December 2017 to lying to investigators -- and continues to lie low because he has not yet been sentenced.

Yet the Twitter messages show that he had conducted his own outreach to at least one lawmaker who attacked the special counsel's investigation and amplified Trump's message that the special counsel probe was a hoax and a "witch hunt."

Gaetz introduced a resolution in 2017 calling for Mueller's resignation, and he led a vocal group of Republicans who sharply criticized the special counsel's legitimacy and pushed for an investigation into the origins of the Trump-Russia probe.

Gaetz is also a regular on the Fox News television circuit, something that the President frequently raises with him when they speak, Gaetz said last year.

While Gaetz says he did not have a relationship with Flynn, he did call for the President to issue a pardon to Flynn and other targets of the Mueller probe last year. "If I were President Trump, I'd pardon Paul Manafort, I would commute the sentence of Michael Flynn and be done with those two," Gaetz said in a Fox News interview.

It's not yet clear what individual connected to Congress was referenced in Thursday's court filings as reaching out to Flynn. The Washington Post reported on Thursday that the person from the Trump administration who contacted Flynn was former Trump lawyer John Dowd. Dowd not respond to CNN's request for comment.

Flynn told Mueller about the discussions, according to the court records, and he gave the special counsel a voicemail recording of one of the conversations, which a federal judge has ordered to be released publicly.

Politics and cooperation

The Twitter messages could complicate Flynn's situation in court.

In December 2018, Flynn went before Judge Emmet Sullivan in US District Court in DC with a more lenient sentencing suggestion from prosecutors than any other Mueller defendant -- little to no jail time. Yet Sullivan seized on a legal brief written by Flynn's lawyers that suggested the FBI agents had faltered in their approach to him. In that brief, Flynn appeared to be sympathizing with Republicans' attacks on the FBI agents he had lied to during a meeting at the White House.

At his sentencing hearing in December, Sullivan questioned whether Flynn had accepted responsibility for his crime. Flynn said "I was aware" that lying to the FBI was a crime.

Flynn asked the judge to postpone his sentencing while he continues to cooperate on other federal matters, and a new date has not been set.