Israeli Foreign Minister Gideon Saar identified the victims as Yaron Lischinsky and Sarah Milgrim.
Lischinsky was a research assistant, and Milgrim organised visits and missions to Israel.
They were leaving an event at the Capital Jewish Museum on Wednesday night when the suspect approached a group of four people and opened fire, Metropolitan Police Chief Pamela Smith said told reporters.
The suspect, Elias Rodriguez, 30, of Chicago, was observed pacing outside the museum before the shooting, walked into the museum after the shooting and was detained by event security, Smith said.
When he was taken into custody, the suspect began chanting "Free, free Palestine", Smith said.
The stunning attack prompted Israeli missions to beef up their security.
The shooting comes as Israel has launched another major offensive in the Gaza Strip in a war with Hamas that has heightened tensions across the Middle East and internationally.
"These horrible D.C. killings, based obviously on antisemitism, must end, NOW!" President Donald Trump posted on social media early Thursday. "Hatred and Radicalism have no place in the USA."
Israeli Prime Minister Benjamin Netanyahu 's office said he was shocked by the "horrific, anti-Semitic" shooting.
"We are witnessing the terrible price of anti-Semitism and wild incitement against Israel," he said in a statement.
Israeli ambassador to the US Yechiel Leiter said the two people killed were a young couple about to be engaged, saying the man had bought a ring with the intent to propose next week in Jerusalem.
Former Israeli ambassador to the US Mike Herzog told Israeli Army Radio that the woman killed was an American employee of the embassy and the man was Israeli.
Attorney-General Pam Bondi said she was at the scene with former judge Jeanine Pirro, who serves as the US attorney in Washington and whose office would prosecute the case.
The statement from Netanyahu's office said he spoke to Bondi, who told him Trump was "involved in managing the incident" and the US would bring the perpetrator to justice.
The war in the Gaza Strip began with the Palestinian militant group Hamas coming out of Gaza on October 7, 2023, to kill 1200 people and take some 250 hostages back to the coastal enclave.
In the time since, Israel's devastating campaign in Gaza has killed more than 53,000 people, mostly women and children, according to local health authorities.
Yoni Kalin and Katie Kalisher were inside the museum when they heard gunshots and a man came inside looking distressed, they said.
Kalin said people came to his aid and brought him water, thinking he needed help, without realising he was the suspect.
When police arrived, he pulled out a red keffiyeh and repeatedly yelled "Free Palestine", Kalin said.
"This event was about humanitarian aid," Kalin said.
"How can we actually help both the people in Gaza and the people in Israel? How can we bring together Muslims and Jews and Christians to work together to actually help innocent people? And then here he is just murdering two people in cold blood."
Last week, the Capital Jewish Museum was among non-profits in Washington awarded funding to increase its security.
The Jewish Federation of Greater Washington CEO Gil Preuss said he was horrified by the shooting and mourned the loss of the two people killed.
"Our hearts are with their families and loved ones, and with all of those who are impacted by this tragic act of anti-Semitic violence," he said.
