WASHINGTON — The Senate Intelligence Committee has issued a subpoena to compel Michael D. Cohen, President Trump’s former lawyer, to appear before the panel next month to formally correct false testimony that he delivered last year about a proposed Trump Organization project in Moscow, one of his lawyers confirmed on Thursday.

The subpoena was disclosed a day after Mr. Cohen pulled out of a public hearing scheduled for Feb. 7 before the House Oversight and Reform Committee, citing in a letter from his lawyer, Lanny J. Davis, verbal attacks by Mr. Trump.

Mr. Cohen’s initial agreement to appear before the Oversight Committee had been voluntary, but he will have little choice in complying with the Senate request. Democrats in charge of the House Oversight and Intelligence committees have signaled in recent days that they may follow suit and issue subpoenas of their own, despite acknowledging Mr. Cohen’s safety concerns.

Unlike the Oversight session, Mr. Cohen’s return to the Senate Intelligence Committee will almost certainly be behind closed doors. The panel has conducted a wide-ranging investigation of Russia’s election interference campaign, and possible ties to the Trump campaign, for roughly two years now largely out of the public eye.