WASHINGTON — The United States attorney’s office for the District of Columbia is dismissing the remaining cases against protesters arrested on the day of Donald J. Trump’s inauguration, ending a legal battle that began more than a year and a half ago.

Federal prosecutors requested Friday in a motion that the charges against the remaining 38 defendants — including one journalist — be dropped. More than 200 people were arrested on Jan. 20, 2017, during demonstrations where some protesters threw rocks and bricks at police officers, set a car on fire and shattered storefront windows.

“After further review, the United States, in the exercise of its discretion, has determined that these matters should be dismissed without prejudice,” read the motion submitted by Jessie K. Liu, the United States attorney for the District of Columbia.

Twenty-one of the people arrested that day have pleaded guilty to charges related to violent protest, including one to felony offenses. That protester, Dane Powell, pleaded guilty to one count of felony rioting and one count of assaulting a police officer. He was sentenced to four months in prison, and was released in October.