WASHINGTON (AP) — A Senate committee has subpoenaed President Donald Trump's former personal lawyer Michael Cohen, his attorney said Thursday, and Cohen intends to comply with the interview demand related to the Russia investigation.

The development comes one day after Cohen postponed his public testimony to a House committee.

Lanny Davis, a lawyer for Cohen, disclosed the subpoena from the Senate Intelligence Committee in a one-sentence statement, and later told The Associated Press in a text message that "we will comply and hope to agree upon reasonable terms, ground rules and a date."

Cohen is set to begin a three-year prison sentence in March.

The Senate committee did not immediately confirm the subpoena, but any interview with Cohen would almost certainly take place in private, in keeping with how the committee generally has conducts Russia-related hearings.

Cohen earlier this week delayed his Feb. 7 appearance before the House Committee on Oversight and Reform on the advice of his legal team, citing ongoing cooperation in special counsel Robert Mueller's Russia investigation and threats against his family. Trump, along with his attorney, Rudy Giuliani, has publicly urged the Justice Department to investigate Cohen's father-in-law , insinuating that Cohen's relative was part of some unspecific criminal activity.

"If he wants to criticize Cohen, he can," Davis said. "Obviously, picking on his family publicly is a way of silencing him or intimidating him. And certainly he has engendered great fear in his extended family, which is why we postponed it."

In an interview Thursday, Davis said the House should take an immediate vote on censuring Trump "as a step before an impeachment investigation," and he pushed for a criminal investigation of Giuliani involving allegations of obstruction, witness intimidation and witness tampering.

The decision to postpone the House interview pushed back the chance of a public airing on additional details of Cohen's relationship with Trump, including hush money payments that Cohen has admitted arranging for two women who say they had sex with the president. Trump has denied the allegation.

Democrats have suggested they may subpoena Cohen to compel his testimony and the committee's chairman, Rep. Elijah Cummings, said Cohen could be brought from prison to appear before Congress.

"We will get his testimony," Cummings said.

Cohen pleaded guilty in November to lying to the Senate intelligence committee about his role in a Trump business proposal in Moscow, acknowledging that he misled lawmakers by saying he had abandoned the project in January 2016 when he actually continued pursuing it for months after that. He has also pleaded guilty to campaign finance violations for his involvement in arranging payments to a former Playboy model and porn actress who had alleged affairs with Trump.

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Sisak reported from New York.