The Senate Intelligence Committee on Thursday subpoenaed Michael Cohen, President Donald Trump's former personal lawyer and fixer, Cohen's attorney, Lanny Davis, confirmed to NBC News.

The move comes a day after Cohen delayed his public testimony before the House Oversight Committee over alleged "ongoing threats against his family from President Trump" and members of his legal team, Davis said in a statement Wednesday.

Cohen will testify on Feb. 12, a source with direct knowledge of the matter told NBC News.

The Senate Intelligence Committee's vice chairman, Virginia Democrat Mark Warner, told reporters on Thursday, “Mr. Cohen was someone who lied to the committee; that got him into the legal jeopardy he started with. He has an enormous number of unanswered questions about Trump Tower and a variety of other items that we need answers to.”

The committee's chairman, Sen. Richard Burr, R-N.C., declined to comment.

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A source with direct knowledge of Cohen's thinking criticized the Senate panel's move as lacking "compassion."

“God bless Elijah Cummings, Adam Schiff and Jerry Nadler for their compassion for Cohen and his family during these crazy times," the source said, referring to the Democratic leaders of key committees in the House. "The Senate Select Intelligence Committee subpoena of Cohen lacks any compassion and exemplifies partisanship and ignores the issue that dominated yesterdays news which was Cohen’s concern and fear for the safety of his family.”

In December, Cohen was sentenced to three years in prison for what a Manhattan federal court judge called a "veritable smorgasbord" of criminal conduct, including making false statements to Congress about the scope and status of a proposed Trump Tower Moscow project. Prosecutors said Cohen provided the Senate Intelligence Committee inaccurate information about the project to minimize links between the president and efforts to build a Trump Tower in Moscow and to give the false impression that the project had ended before the Iowa caucuses in February 2016.

Davis said on MSNBC's "Andrea Mitchell Reports" Thursday that Cohen “has to comply with subpoenas" and will have "reasonable conversations" with lawmakers. Davis also said Cohen is more than willing to testify before the House committee but remains concerned about threats to his family.

Davis also criticized the president and his personal lawyer Rudy Giuliani for targeting Cohen's relatives in interviews.

“This is classic mob technique to send a signal to the individual who Mr. Trump has called a ‘rat’ for telling the truth," he said. "Now, that word ‘rat’ comes directly out of organized crime. It’s also a signal to other inmates in a potential prison situation."

“But the family of Michael Cohen has been called out by Donald Trump," Davis said. "Once again, he ducks or lies about what he knows he’s done, which is to attack a father-in-law and wife as a way of getting to Mr. Cohen, and that is called witness tampering, obstruction of justice.”

Giuliani claimed Sunday on CNN's "State of the Union" that Cohen's father-in-law, Fima Shusterman, might have ties to organized crime and that he was involved in criminal activity with Cohen. Last week, Trump reacted to a disputed BuzzFeed report that said he directed Cohen to lie in his congressional testimony by making a reference to Cohen's father-in-law, who reportedly loaned roughly $20 million to a Chicago cab mogul who was mentioned in FBI search warrants for Cohen.

Kevin Corke, @FoxNews “Don’t forget, Michael Cohen has already been convicted of perjury and fraud, and as recently as this week, the Wall Street Journal has suggested that he may have stolen tens of thousands of dollars....” Lying to reduce his jail time! Watch father-in-law! — Donald J. Trump (@realDonaldTrump) January 18, 2019

In a Fox News interview last month, Trump also asked whether Cohen might have made "a deal to keep his father-in-law out [of legal trouble]?"

On Wednesday, Trump told reporters that Cohen had delayed his testimony before the House committee because he was "threatened by the truth."

On Thursday, Davis called Giuliani "mentally unstable" and said he's "a prosecutor who would prosecute what he just did," referring to the claims Giuliani made on CNN. Davis declined to say if Cohen's family would pursue legal action against Giuliani but called on Congress to vote on a resolution of censure to reprimand Trump.

"You can go after Mr. Cohen, if that’s their design, because Mr. Cohen’s an adverse witness," Davis said. "What do his father-in-law and his wife have to do with anything — other than the crime of witness tampering, intimidation, and corrupt intent to try to deter Mr. Cohen from telling the truth? And I hope the Senate and the House, they can vote a resolution of censure, and Mr. Giuliani can be indicted and certainly criminally investigated for doing what he just did, that is prima facie a crime to threaten a witness before Congress."