President Donald Trump on Monday suggested that House Intelligence Committee Chairman Adam Schiff could face "arrest for treason" over his recent statement about Trump's call with Ukraine's president.

"Rep. Adam Schiff illegally made up a FAKE & terrible statement, pretended it to be mine as the most important part of my call to the Ukrainian President, and read it aloud to Congress and the American people," Trump tweeted.

"It bore NO relationship to what I said on the call. Arrest for Treason?" he added.

Neither the White House nor a spokesman for Schiff, D-Calif., immediately responded to CNBC's request for comment on the president's tweet.

The fiery tweet accusing Schiff — a leading voice on the House's impeachment inquiry into Trump — of "illegally" misrepresenting him came days after the president said at a private staff event that "we used to handle" spies and treason "a little differently than we do now."

He was referring to the sources used by a whistleblower, who filed a bombshell complaint last month alleging Trump was "using the power of his office to solicit interference from a foreign country in the 2020 U.S. election" by asking Ukrainian President Volodymyr Zelensky to investigate rumors of wrongdoing against former Vice President Joe Biden and his son Hunter.

In the same call, Zelensky had suggested Ukraine was about ready to buy weapons from the U.S. military. Trump responded, "I would like you to do us a favor though because our country has been through a lot and Ukraine knows a lot about it." Trump appeared to be referring in that portion of the call to the origins of special counsel Robert Mueller's Russia probe. He suggested he would have Attorney General William Barr "call you or your people" as part of the proposed investigation.

Reporting about the complaint, which was made public last week along with a memorandum of Trump's July 25 call with Zelensky, led House Speaker Nancy Pelosi, D-Calif., to back an impeachment inquiry into the president.

Dozens of Democrats came out in favor of an inquiry as details about the call came to light. Nearly the entire House caucus now supports an impeachment inquiry.

Schiff has characterized Trump's call with Zelensky as a "classic organized crime shakedown," and took that analogy further in a contentious hearing Thursday with acting Director of National Intelligence Joseph Maguire.

Maguire had initially declined to share the whistleblower's complaint with Congress, leading Democrats to accuse his office of breaking the law. While the intelligence commmunity's inspector general had found the complaint to be "urgent" and "credible," the Justice Department determined it did not meet the legal threshold of "urgent" and therefore did not need to be immediately handed over.

Maguire said he was doing what seemed prudent in an "unprecedented" situation, while Democrats slammed him for taking the complaint to an agency whose top official was implicated in the complaint.

In the hearing, Schiff delivered a self-described "parody" of the call using mobster-like language.

"Shorn of its rambling character, and in not so many words, this is the essence of what the president communicates," Schiff began.

"We've been very good to your country. Very good. No other country has done as much as we have. But you know what, I don't see much reciprocity here. I hear what you want. I have a favor I want from you though. And I'm going to say this only seven times, so you better listen good. I want you to make up dirt on my political opponent, understand? Lots of dirt, on this and on that," Schiff said in the parody of the call.

"I'm going to put you in touch with people, and not just any people. I'm going to put you in touch with the attorney general of the United States — my attorney general, Bill Barr — he's got the whole weight of the American law enforcement behind him. And I'm going to put you in touch with [Trump's personal lawyer, Rudy Giuliani], you're going to love him. Trust me. You know what I'm asking, so I'm only going to say this a few more times, in a few more ways. And by the way, don't call me again. I'll call you when you've done what I asked."

"This is, in sum and character, what the president was trying to communicate," Schiff said.

In the U.S. Constitution, treason is defined as "levying war against" the United States or "in adhering to their Enemies, giving them Aid and Comfort." The maximum punishment for treason in the U.S. criminal code is death.