In early January, Michael D. Cohen, President Trump’s personal lawyer, filed a pair of lawsuits claiming that the political research firm Fusion GPS and the website BuzzFeed had defamed him by promoting the so-called Steele dossier, an intelligence report that alleged connections between Mr. Trump’s associates and Russia. The dossier depicted Mr. Cohen as a central figure in what it described as a conspiracy.

In the suits, Mr. Cohen complained that Fusion GPS had disseminated the dossier to reporters and that BuzzFeed put it on the internet, even though both companies knew that it contained what Mr. Cohen believed were lies.

But much has changed in the past three months. Just last week, Mr. Cohen discovered that he is now the subject of a federal investigation seeking to determine if he broke the law by trying to tamp down scandals involving women who claimed they had affairs with Mr. Trump. Because of that investigation, Mr. Cohen’s lawyer dropped both lawsuits in a sudden move on Wednesday night.

“The decision to voluntarily discontinue these cases was a difficult one,” the lawyer, David M. Schwartz, said on Thursday. While Mr. Schwartz insisted that he still believes that BuzzFeed and Fusion GPS defamed Mr. Cohen, he added, “Given the events that have unfolded, and the time, attention and resources needed to prosecute these matters, we have dismissed the matters, despite their merits.”