On Friday, The Globe filed suit against Ms. Sargent seeking to compel her to provide the date of the text exchange and the context in which it was written, a request to which she has yet to respond.

While Ms. Sargent has indicated that the exchange took place while Mr. McGrory was her supervisor, the suit says that an investigation by the Globe had found so far that “this exchange did not take place between McGrory and Sargent during the time when Sargent was employed by The Globe.”

Ms. Sargent, 39, declined in a phone interview to comment on the record because of possible legal action. But she said in an earlier statement to The Globe: “If Brian McGrory truly does not believe he has ever acted inappropriately with anyone at The Boston Globe, then he and I have a remarkably different understanding of what is — and is not — appropriate.”

In his statement, Mr. McGrory, 56, said that he and Ms. Sargent had dated years ago but that they were not working together at the time. Mr. McGrory said he had no recollection of the text exchange Ms. Sargent had posted.

Mr. McGrory’s lawyer, Martin F. Murphy, said in a letter to Ms. Sargent’s lawyer, a copy of which was obtained by The New York Times, that her message on Twitter falsely cast Mr. McGrory “as part of that group of men who have, in fact, used their positions, to sexually harass or assault women.” He said these “false and defamatory statements” could lead to legal action.

Late last year, when The Globe was contending with critiques of its handling of the departure of Mr. O’Sullivan, the political reporter, Mr. McGrory had acknowledged the episode’s effect on the newspaper’s standing. “While our discussions on the O’Sullivan matter were mostly focused on proof, fairness and spectrums of misconduct,” Mr. McGrory wrote in his front-page note to readers, “there’s now a fairly obvious realization that I didn’t focus enough on another very important factor: The Globe’s institutional credibility.”

“Please know that we’ve learned vital lessons about holding ourselves to a higher standard, lessons that I pledge will be vigorously applied to our coverage of these and many other issues going forward,” he added.