House Intelligence Committee Chairman Adam Schiff told CBS's "Face the Nation" on Sunday that he will subpoena President Donald Trump's former longtime attorney Michael Cohen to testify before his committee "if necessary."

"Yes, we've given Michael Cohen a date that we'd like him to come in either voluntarily or, if necessary, by subpoena," Schiff, D-Calif., told CBS's Margaret Brennan.

Cohen is already slated to testify before the House Oversight Committee next month prior to the start of his three-year prison sentence. In a statement announcing his testimony to that congressional panel, Cohen said he looked "forward to having the privilege of being afforded a platform with which to give a full and credible account of the events which have transpired."

Last year, Cohen pleaded guilty to nine federal felonies, including two campaign-finance violations stemming from his facilitation of hush payments to women who allege affairs with Trump and one related to making false statements to Congress about the scope and status of a proposed Trump Tower project in Moscow so he could be consistent with Trump's public pronouncements.

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Trump has denied any affairs and has accused Cohen of lying to get a reduced sentence. Following Cohen's sentencing, Trump defended his efforts to build a Trump-branded tower in Russia while running for president of the United States as "very legal" and "very cool."

In a disputed story, BuzzFeed reported last week that Trump ordered Cohen to lie to Congress about the proposed Trump Tower Moscow project. The report cited two federal law enforcement officials involved in an investigation of the matter and stated that special counsel Robert Mueller had documents and other evidence to back up the assertion.

But on Friday, Mueller spokesperson Peter Carr disputed BuzzFeed's report in an unprecedented statement from the Special Counsel's Office, saying its "description of specific statements to the Special Counsel’s Office, and characterization of documents and testimony obtained by this office, regarding Michael Cohen’s Congressional testimony are not accurate."

BuzzFeed is standing by its story, but the news site has yet to publish a follow-up on its original report.

Speaking with Brennan on Sunday, Schiff pointed to comments Trump's personal attorney Rudy Giuliani made on a pair of Sunday show appearances and said he would further probe the matter.

"I guess this morning [Giuliani] said that he's not writing off the possibility that the president did talk to Michael Cohen about his testimony or that others may have as well," Schiff said. "And we need to know exactly what those conversations were. They're certainly not protected by any kind of a privilege. And if anyone was instructing — whether it was the president or other people affiliated with the White House or the Trump Organization — encouraging a witness to lie, we need to know about it."

"And I will say one other thing," Schiff continued. "We know that the president's public statements have been false as it pertains to his business dealings with Russia. And so the combination of his public falsehoods with false testimony before Congress certainly contributes to a picture of obstruction of justice."

Giuliani said Sunday that he was "100 percent certain" that Trump never directed Cohen to lie to Congress, but Giuliani did leave the door open to the two men discussing Cohen's 2017 testimony ahead of time.

If Trump did have discussions with Cohen about his testimony, Giuliani told CNN's Jake Tapper on "State of the Union" that it "would be perfectly normal."

"And so what if he talked to him about it?" Giuliani added.