Chicago-born suspect Elias Rodriguez, 30, is accused of opening fire on a group of people on Wednesday night as they left an event for young diplomats hosted by the American Jewish Committee, an advocacy group that supports Israel and confronts anti-Semitism, according to its website.
Officials said he was heard chanting "Free Palestine" after he was taken into custody.
The two victims struck by gunfire and killed were identified as Yaron Lischinsky and Sarah Lynn Milgrim, a young couple about to become engaged to be married.
Friends and members of advocacy groups they belonged to said the pair were committed to building bridges between Arabs and Jews in hopes of ending bloodshed in the Middle East.
After the shooting, Israeli embassies around the world immediately stepped up security.
FBI Deputy Director Dan Bongino posted on social media that investigators were "aware of certain writings allegedly authored by the suspect" and hoped to soon have updates regarding their authenticity.
Bongino's statement appeared to refer to a manifesto signed with Rodriguez's name that was posted to an anonymous X account on Wednesday night shortly before the shooting.
Posted with the title "Escalate For Gaza, Bring The War Home," it condemned Israel's killing of tens of thousands of Palestinians since the October 2023 Hamas attacks and discussed the morality of "armed" action.
"In the wake of an act people look for a text to fix its meaning so here's an attempt," the document read.
"The atrocities committed by Israelis against Palestine defy description and defy quantification."
FBI Director Kash Patel called the bloodshed an "act of terror," although US Attorney General Pam Bondi told reporters that authorities believe the suspect acted alone.
Israel has faced sustained international condemnation for its escalating military offensive in the Gaza Strip while Jewish advocacy groups have warned of a rise in anti-Semitic incidents globally.
Investigators also delved into apparent political affiliations of the suspect, who worked for a healthcare nonprofit and was believed to have had past ties to leftist extremist groups.
According to an account by Washington Metropolitan Police Chief Pamela Smith, a man shot at a group of four people with a handgun, hitting both the victims.
He was seen pacing outside the museum prior to the shooting, little more than 2km from the White House.
"Once in handcuffs, the suspect identified where he discarded the weapon, and that weapon has been recovered, and he implied that he committed the offence," Smith said, adding that he had had no previous contact with police.
FBI agents were seen at his apartment in Chicago on Thursday, where law enforcement blocked off the street.
Witness Katie Kalisher, 29, said she was among people in the museum who were chatting to a man who entered looking very scared after gunshots were heard outside when he suddenly pulled out a keffiyeh scarf.
"He says, 'I did it. I did it for Gaza, free, free Palestine.' And he's chanting this. And then suddenly the police come in and they arrest him," said Kalisher, a jewellery designer.
Rodriguez was once affiliated with the Party for Socialism and Liberation, according to a post from the group on X.
The group said that Rodriguez had a brief association with a PSL branch that ended in 2017 and that they knew of no contact with him in more than seven years.
"We have nothing to do with this shooting and do not support it," the organisation said.
