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 fights antisemitism.
Officials said he was heard chanting "Free Palestine" after he was taken into custody.
In addition to first-degree murder, Rodriguez was charged on Thursday in a criminal complaint with murder of foreign officials, causing death with a firearm and discharging a firearm in a crime of violence.
The charges were filed in federal court as FBI and police investigators pored over apparent writings and political affiliations of the suspect.
The two victims struck by gunfire and killed were identified as Yaron Lischinsky, 30, and Sarah Lynn Milgrim, 26, a young couple about to become engaged.
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 Gaza military offensive, while Jewish advocacy groups have warned of a rise in antisemitic 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 far-left 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 two kilometres 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 Rodriguez 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.
US President Donald Trump condemned the shooting.
"These horrible D.C. killings, based obviously on antisemitism, must end, NOW!" he said in a message on Truth Social. "Hatred and Radicalism have no place in the USA."
Israeli Prime Minister Benjamin Netanyahu said his heart ached for the families of the victims, "whose lives were cut short in a moment by an abhorrent antisemitic murderer".
The shooting is likely to fuel polarisation in the United States over the war in Gaza between supporters of Israel and pro-Palestinian demonstrators.
An invitation for Wednesday's American Jewish Committee event said the gathering brought together young Jewish professionals and diplomats for presentations focused on efforts to address humanitarian crises throughout the Middle East and North Africa.
