Lawyers for Jack Smith, the former special counsel who investigated Donald J. Trump, have struck back for the first time against some of the accusations conservatives have leveled against him, denouncing an ethics complaint as “imaginary and unfounded.”

For months, Mr. Smith has remained silent as the president and some of his senior advisers, including top Justice Department officials, publicly attacked him, accusing Mr. Smith of engaging in wrongdoing for overseeing two criminal inquiries and indictments of Mr. Trump. The investigations involved whether Mr. Trump mishandled classified documents after he left office as well as his efforts to overturn the results of the 2020 election.

On Monday, Mr. Smith’s legal team sent a letter to the Office of Special Counsel, which has no affiliation with Mr. Smith’s former position. The Office of Special Counsel conducts ethics investigations of government employees, primarily into whether people have violated the Hatch Act, which bars federal workers from using their jobs to work on behalf of a political campaign.

Senator Tom Cotton, Republican of Arkansas, persuaded the agency to investigate whether Mr. Smith, in seeking to quickly bring Mr. Trump to trial, violated the law. Mr. Smith’s conduct, he claimed, appeared “to have no rationale except for an attempt to affect the 2024 election results.”

Mr. Smith and his lawyers, Lanny A. Breuer and Peter Koski, fired back in a three-page letter to the acting special counsel, Jamieson Greer.