WASHINGTON — Two Democratic senators disclosed on Thursday that they had asked James B. Comey, the former F.B.I. director, to open a criminal investigation into whether Attorney General Jeff Sessions perjured himself when he falsely said at his confirmation hearing that he “did not have communications with the Russians” last year.

The senators, Patrick J. Leahy of Vermont and Al Franken of Minnesota, released three letters to the F.B.I. that they privately sent in March, April and May. The letters also showed they had been expecting a briefing from Mr. Comey on May 12 but never got it because President Trump abruptly fired him three days earlier.

“We served with the attorney general in the Senate and on the Judiciary Committee for many years,” Mr. Franken and Mr. Leahy said in a joint statement accompanying the release of their letters. “We know he would not tolerate dishonesty if he were in our shoes. If it is determined that the attorney general still has not been truthful with Congress and the American people about his contacts with Russian officials during the campaign, he needs to resign.”

The dispute centers on Senate Judiciary Committee confirmation testimony Mr. Sessions gave in January, when he told Mr. Franken that he did not have any contacts with Russians last year. In fact, Mr. Sessions met at least twice in 2016 with the Russian ambassador to the United States, Sergey I. Kislyak: once at a reception at the Republican National Convention in July, and in Mr. Sessions’s Senate office in September.