The gunfire erupted in the Columbia Heights neighborhood, about two miles (three km) from the White House late September 19.
According to the police, the incident was reported at around 10:06 pm on Thursday.
In the other shooting later Thursday, two men and a woman were wounded, but an update on their conditions was not available early Friday.
Investigation is on whether the second nearby shooting is related to the first one, Emerman said.
Police say that the incident is not considered an "active shooter" situation.
The suspects were last seen near the scene of the shooting, police said.
One of them died, Stuart Emerman, commander of the police department's third district, was quoted as saying by the report.
Reports said that the local channel, WJLA-TV, posted images on Twitter of ambulances carrying victims from the scene.
They're also looking for a light-colored Nissan sedan with unknown tags as possibly involved as well.
In the Rhode Island Avenue shooting, a man was found unconscious and not breathing.
Two men and a woman were shot around 10:30 p.m. and rushed to area hospitals.