The first attack occurred about 6 p.m. yesterday (Wednesday) at 1500 Isherwood St. NE.
The second reported attack took place about 7:40 p.m. on the 1500 block of Massachusetts Avenue SE.
A man and his friends were arguing with another man when the lone man whipped out a knife, police said. The victim received non-life-threatening injuries.
The third attack took place about 12:15 a.m. today in Spirit of Justice Park, just south of the Longworth and Rayburn House Office Buildings, police said.
A black man with dreadlocks, who stands 5-foot-5 to 5-foot-7, is being sought for the first attack, police said.
A black man about 20 years old, who stands 5-foot-8. is being sought for the second stabbing. He was last seen wearing a black Helly Hansen jacket and dark fatigue pants.
And for the third incident, police are seeking two black men who were wearing white shirts and blue jeans.
Police did not immediately respond to an inquiry about what preceded the first and third attacks.