A vigil was held on Monday for Aaron Bushnell outside the Israeli embassy in DC
Aaron Bushnell, 25, was taken to hospital after Secret Service officers extinguished the flames.
Before setting himself alight in what he called an "extreme act of protest", he said he would "no longer be complicit in genocide".
No embassy staff members were injured in the incident, a spokeswoman said.
A Pentagon spokesman called the incident, which happened at 13:00 local time (18:00 GMT), a "tragic event".
In a video aired live on streaming site Twitch, Mr Bushnell, who was dressed in military uniform, identified himself and said he was a serving member of the Air Force.
Earlier, he had emailed a number of reporters and left-wing and anarchist news websites. The Atlanta Community Press Collective, one of the groups that received the email, provided a copy to the BBC.
"Today, I am planning to engage in an extreme act of protest against the genocide of the Palestinian people," the email read, warning it would be "highly disturbing".
Mr Bushnell was taken to the hospital in a critical condition.
A bomb disposal unit was sent to the site over concerns about a suspicious vehicle that could have been connected to the individual. This was declared safe after no hazardous materials were found.
Washington police said officers were working with the Secret Service and the Bureau of Alcohol, Tobacco, Firearms and Explosives to investigate the incident.
Mr Bushnell, of San Antonio, Texas, was raised in Massachusetts and attended public schools on the Cape Cod peninsula, according to a statement from a local school district.
The Air Force would not confirm details of Mr Bushnell's service, citing family notification policies but Stars and Stripes, a military newspaper, reported that he had held the rank of senior airman.
In his Linkedin profile, Mr Bushnell stated that he had graduated from Air Force basic training "top of class" in November 2020 and that he had been seeking "to transition out of the US Air Force into software engineering".
The Israel-Gaza war erupted on 7 October last year when Hamas gunmen infiltrated southern Israel, killing about 1,200 people and taking 253 others hostage.
Israel responded by launching a military campaign in Gaza, during which 29,300 people have been killed, according to the Hamas-run health ministry.
As of mid-January, 1.9 million civilians in Gaza have been displaced amid Israel's military operations, according to the UN, accounting for 85% of its population.
In an interview with CBS News on Sunday, Israeli Prime Minister Benjamin Netanyahu defended the offensive in the face of international criticism, saying America would be "doing a hell of a lot more" if it had suffered such an attack.
It is not the first time someone has set themselves on fire in front of an Israeli diplomatic mission in the US since the intensification of the conflict.
In December, a protester self-immolated in front of the Israeli consulate in the US state of Georgia.
A Palestinian flag found at the scene was part of the protest, police said.
-- Courtesy of BBC News