President Donald Trump quickly condemned the attack.
According to AFP, the shooting broke out on the sidewalk outside the capital Jewish Museum in the heart of Washington. The venue hosted a social event for young professionals and diplomatic staff.
The victim was a young couple planning a marriage, the Israeli ambassador said.
A video clip circulating on social media showed a young bearded man wearing a jacket and a white shirt screaming “free and free Palestine” that was taken to police.
Police confirmed that the gunman stepped into the museum after the shooting and was taken into custody.
“We believe the shooting was committed by one of the suspects currently in custody,” Washington Police Chief Pamela Smith told reporters.
“Before the shooting, the suspect was observed to travel back and forth outside the museum. He approached a group of four, produced handguns and fired.
“After the shooting, the suspect entered the museum and was taken into custody by event security.”
She said the handcuffed suspect identified the location where he abandoned his weapon and chanted “free, free Palestine.”
Police identified him as Elias Rodriguez, 30, from Chicago.
“I’m devastated by the Washington scene,” Isaac Herzog, head of the Israeli regime, said in a statement.
MNA