The man poured a can of petrol on himself before setting himself on fire on Friday. Police are investigating the motive for the act.
Passing joggers used their shirts to try to extinguish the flames.
The man was so badly burned that he will have to be identified using DNA and dental records, police spokesman Araz Alali said.
Officials said earlier that the man was still conscious when he was flown from the Mall to hospital on Friday.
The incident came a day after police shot dead a woman after chasing her car through the centre of Washington DC.
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