On Monday, a spokesman for Mr. Ellison’s campaign referred to Sunday’s statement. Mr. Ellison, who lost a 2017 bid to become the party’s chairman, announced in June that he was stepping down after 11 years in Congress to run for attorney general. A representative for the Democratic National Committee did not respond to a request for comment.

It was still unclear on Monday whether there would be immediate political consequences for Mr. Ellison, who has been endorsed by Senator Bernie Sanders. His opponents in Tuesday’s primary had not called on him to drop out, but two of them called for an immediate response. Another said if a video exists, it should be given to the police.

A women’s advocacy group called for him to withdraw the race.

In the email she sent on Sunday to The Times, Ms. Monahan said it had been “a very difficult time for me and my family” and she “was not in a place to talk.” The Monahans did not respond Monday to messages for further comment or an opportunity to review the messages and video.

Minnesota Public Radio said it reviewed more than 100 messages between Mr. Ellison and Ms. Monahan, which it said had been provided to the news organization by Ms. Monahan. “There is no evidence in the messages reviewed by MPR News of the alleged physical abuse,” the news organization reported.

Mr. Monahan told the Star Tribune that he did not have a copy of the video, but stood by what he said he saw.

Ms. Monahan said in her email that she started to suffer from post-traumatic stress disorder around 2014, and was in poor health when the relationship ended, a point for which they gave different dates.