Ms. Montgomery’s initial tweet drew public criticism from some Washington Post employees. She later tweeted that she regretted her initial post and said she didn’t intend to question the validity of accusations against Mr. Roethlisberger. Mr. Roethlisberger has denied allegations of sexual assault.

Ms. Montgomery was given a verbal warning this past weekend, the Post spokeswoman said. The Post is planning to revise its social-media policy as soon as it fills a vacant standards-editor position, she said. Ms. Buzbee’s remarks about reprimanding Ms. Montgomery came during calls this week with groups of Post employees, people familiar with the discussions said.

Ms. Montgomery referred a request for comment to the Post.

Felicia Sonmez, a reporter at the newspaper, was among the critics of Ms. Montgomery’s tweet. She said in her own post on Twitter that the Washington Post also reported on allegations of sexual assault against Mr. Roethlisberger and asked whether employees would feel safe reporting harassment to editors who make similar comments.

Ms. Sonmez sued the Washington Post and several of its top editors last year alleging the Post discriminated and retaliated against her. Ms. Montgomery is one of the editors named in Ms. Sonmez’s lawsuit. In her lawsuit, Ms. Sonmez says the Washington Post unfairly prevented her from covering stories related to sexual harassment and assault because they believed she had a conflict of interest as a sexual-assault survivor.

A Washington Post spokeswoman declined to comment on Ms. Sonmez’s lawsuit. Ms. Sonmez had no immediate comment.

Write to Benjamin Mullin at Benjamin.Mullin@wsj.com and Alexandra Bruell at alexandra.bruell@wsj.com