The incident allegedly took place five years ago, while Thrush was a reporter for Politico. He joined the New York Times in January to cover the Trump administration, according to the newspaper.
McGann, who was an editor at Politico when the alleged incident took place, said Thrush later told colleagues that their encounter went the other way and that he rejected advances from her. He reiterated his recollection to Vox, saying in a statement that "the encounter described was consensual, brief, and ended by me."
Three other women recounted similar tales to Vox involving Thrush. They declined to be identified.
"I apologize to any woman who felt uncomfortable in my presence, and for any situation where I behaved inappropriately," Thrush told Vox Sunday in an emailed statement. "Any behavior that makes a woman feel disrespected or uncomfortable is unacceptable."
Officials with the Times said Monday that they were opening an investigation into the alleged incidents, one of which reportedly took place in June, after Thrush joined the newspaper.
"The behavior attributed to Glenn in this Vox story is very concerning and not in keeping with the standards and values of The New York Times," the Times officials said in a statement. "We intend to fully investigate and while we do, Glenn will be suspended."
Thrush said he was “deeply sorry” for an encounter that happened in June, in which a woman said Thrush began kissing her on the street after they had been in a bar. Thrush said he hasn’t had alcohol since the event, which he called “life changing.”
Another woman in the story talks about a consensual drunken encounter with Thrush five years ago that left her rattled, and a fourth woman who was surprised by an unexpected kiss.
Thrush worked as the chief political correspondent at Politico and as a senior staff writer for Politico Magazine before joining the Times staff. He previously worked at Newsday.
The Associated Press contributed to this report.