The Manhattan federal court lawsuit was filed a day after CNN sued the Justice Department in Washington, seeking the same information.
Both actions seek documents Comey told the Senate he created earlier this year immediately after meetings and conversations with the president.'
Comey said he typed notes describing the conversations because he was worried Trump "might lie" later about them. He testified that he leaked information about the notes through a friend to the Times to increase pressure for the appointment of a special prosecutor after he concluded Trump's administration "defamed" him and the FBI after his May 9 firing.
Former FBI head Robert Mueller was appointed as special counsel a day after a report stemming from the notes was published.
Comey said the notes contain his recollections that Trump asked for his loyalty when they met for a January dinner and then urged him during a private meeting in the Oval Office two weeks later to drop an investigation into former National Security Adviser Michael Flynn. Trump has disputed both claims, saying flatly that he never asked Comey to drop the Flynn probe.
The Times and CNN both said in their lawsuits that the FBI has not turned over documents and has failed to properly respond to their Freedom of Information Act requests. They asked judges to order the FBI to produce the records.
The Associated Press also filed a FOIA request for the documents but has not received any documents and has not sued.