Police said the man was wounded in the hand or arm and was taken into custody. Newsham said a gun was recovered.
The shootings minutes apart shortly after 5 p.m. complicated rush-hour traffic along the busy H Street corridor and forced police to close streets in the area.
Newsham said officers heard the first shots and acted immediately. He described their actions in apprehending the suspect as “heroic.”
Shootings in the District’s downtown business area are rare, and Newsham described it as the “very brazen act of a violent offender.”
Police did not immediately publicly identify the victim or the man who was arrested.
Witnesses on social media recounted a chaotic scene, describing officers with guns drawn chasing the suspect past churches, a theater, a law firm and restaurants.
A man who declined to give his namesaid he was waiting for a bus at 11th and H streets when he heard three to four gunshots.
“I didn’t know at first it was gun shots until I started to smell the gun powder and saw people running,” he said in a direct message on Twitter. “It was very terrifying. Once I realized what was going on I ran to the hotel parking lot down the street.”
The incident downtown was followed by another shooting about an hour later when at least one D.C. police officer shot and wounded a man during an exchange of gunfire in the Petworth area of Northwest Washington.
The incident unfolded in the area of Grant Circle about 5:45 p.m. when officers were called to investigate the sound of gunshots, police said. Officers encountered a man they described as a suspicious person who then fired at police, said Dustin Sternbeck, a police spokesman.
Officers returned fire and struck the man multiple times, Sternbeck said. It was not immediately clear how many officers fired.
Police recovered a firearm from the scene, Sternbeck said. The wounded man was taken to a hospital and was in surgery Thursday night.
The incidents in Chinatown began on 8th Street between H and G streets, less than a block from the Gallery Place Metro station. Newsham said two men were arguing when one pulled out a gun and shot the other several times. Other officials said the victim was shot in the head.
Newsham said officers were close enough to hear the shots, and they ran to the scene and chased the man west. He said at least two officers and the man exchanged gunfire in the 700 block of 10th Street NW, between G and H streets. No officers were injured.
The wounded man then ran to the 1000 block of H Street NW, nearly in front of the Grant Hyatt, where officers were able to subdue and arrest him.
Newsham said it was not immediately clear whether the gunman and the victim knew each other or why they were arguing.
Paul Duggan and Joe Heim contributed to this report.