U.S. Rep. Matt Gaetz (R-FL) speaks during a rally hosted by FreedomWorks September 26, 2018 at the West Lawn of the Capitol in Washington, DC.

He told reporters "we'll see" if the committee's chairman, Rep. Elijah Cummings, D-Md., would allow him to ask questions. Gaetz for some time sat in the hearing room as Cohen testified.

Gaetz himself showed up for Cohen's testimony at the House Oversight and Government Reform Committee despite not being a member of that committee.

The Florida Bar's probe came to light as a Democratic congressional colleague of Gaetz's suggested that he be referred for his tweet for possible discipline by the House Ethics Committee for "witness intimidation and tampering," and that he might face criminal prosecution for the tweet.

Rep. Matt Gaetz of Florida is under investigation by his state's lawyer oversight group for a potentially threatening tweet that the Republican congressman directed at President Donald Trump's former personal attorney Michael Cohen in advance of his testimony before a House committee Wednesday.

Gaetz on Tuesday tweeted directly at Cohen, using Cohen's Twitter handle, a message that said: "Hey @MichaelCohen212 - Do your wife & father-in-law know about your girlfriends?"

"Maybe tonight would be a good time for that chat. I wonder if she'll remain faithful when you're in prison. She's about to learn a lot..." Gaetz wrote.

Gaetz's tweet was almost instantly criticized as possible witness tampering of Cohen, whose lawyer weeks ago accused Trump and the president's current attorney, Rudy Giuliani, of trying to intimidate Cohen into not testifying before Congress.

Cohen's lawyer, Lanny Davis, said, "We will not respond to Mr. Gaetz's despicable lies and personal smears, except to say we trust that his colleagues in the House, both Republicans and Democrats, will repudiate his words and his conduct."

Gaetz, a close ally of Trump, initially defended his tweet, saying "This isn't witness tampering. This is witness testing."

But he deleted it and apologized online hours later after House Speaker Nancy Pelosi, D-Calif., issued a statement encouraging all members of Congress to avoid making statements that could harm committees' ability "to obtain the truthful and complete information necessary to fulfill their duties."

It "was NOT my intent to threaten, as some believe I did," Gaetz said in a tweet. "I'm deleting the tweet & I should have chosen words that better showed my intent. I'm sorry."

The Daily Beast first reported that Gaetz was under investigation by The Florida Bar for the deleted tweet in response to a complaint by a member of the general public.

"The Florida Bar is aware of the comments made in a tweet yesterday by Rep. Matt Gaetz, who is a Florida Bar member, and I can confirm we have opened an investigation," the group said in a statement to CNBC.

"Any time the words or actions of a Florida lawyer result in complaints, The Florida Bar will fully investigate those complaints through its established grievance process to determine if Bar rules have been violated," the group said. "If rules have been violated, The Florida Bar will vigorously pursue appropriate discipline by the Florida Supreme Court."

Florida Bar rules of conduct say that attorneys "should use the law's procedures only for legitimate purposes and not to harass or intimidate others."

During Cohen's testimony on Wednesday, Rep. Stacey Plaskett, D-Virgin Islands, told Cohen, " I want to apologize for the inappropriate comments and tweets that have been made by other members of this body."

"And as a former prosecutor, and as former counsel on House ethics, I think that at the very least there should be a referral to the Ethics Committee of witness intimidation and tampering under [U.S. Criminal Code section] 1512 of my colleague Matt Gaetz, and it may be, possibly, him being referred for criminal prosecution."

Gaetz's spokeswoman, in a response to a request for comment, said, "It seems that the Florida Bar, by its rules, is required to investigate even the most frivolous of complaints."