The same is true of Mr. Cohen, who has vehemently denied any role in the conspiracy claimed in the dossier. In August, Mr. Cohen went so far as to give Congress a point-by-point rebuttal of the dossier’s allegations that he has deep ties to Russian officials. He specifically denied one of the best-known allegations against him — that he secretly met in Prague with a Russian official last summer.

In the lawsuit, Mr. Cohen’s lawyers say that Fusion acted recklessly and then disseminated the dossier to reporters without being able to back up its explosive claims.

Mr. Cohen was “collateral damage in a U.S. political operation,” the lawsuit says.

“We want to the courts to bring to a head because nobody else was going to bring this to a head,” said David. M Schwartz, Mr. Cohen’s lawyer. “This is the way Michael Cohen will get back his reputation — through the courts.”

Neither Fusion nor Mr. Steele had any immediate comment on Mr. Cohen’s lawsuit.

Ben Smith, the editor in chief of BuzzFeed News, wrote in an op-ed article published late Tuesday by The Times that “a year of government inquiries and blockbuster journalism has made clear that the dossier is unquestionably real news.”

He defended BuzzFeed’s decision to publish the dossier, despite having not verified the accuracy of its contents. Without it, many Americans would not have had the context necessary to fully understand the Russia investigations, he wrote.

“We strongly believed that publishing the disputed document whose existence we and others were reporting was in the public interest,” he wrote.

Mr. Cohen is not the first to sue BuzzFeed over the dossier. The news organization also faces a lawsuit by Aleksej Gubarev, a Russian technology executive named in the dossier. As part of that case, lawyers for Mr. Gubarev, who runs XBT, a technology company based in Luxembourg, have subpoenaed both Fusion and Mr. Steele for documents about the dossier and their communications with the news media.

Mr. Gubarev is mentioned at the end of the dossier, which claims that he and his company were involved in hacking operations against the leadership of the Democratic Party.