Forty-one bodies had been pulled from the river as of Friday afternoon, including 28 that had been positively identified, Washington DC fire chief John Donnelly Sr said at a news conference.
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He said next of kin notifications had been made to 18 families, and that he expects that all 67 of the bodies of the dead will eventually be recovered.
“It’s been a tough response for a lot of our people,” Mr Donnelly said, noting that more than 300 responders were taking part in the effort at any one time.
Investigators have already recovered the cockpit voice recorder and flight data recorder of the American Airlines plane, which struck the helicopter as the plane was coming in for a landing at the airport next to Washington.
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49:10
Plane Crash: What went wrong?
Officials are scrutinising a range of factors in what National Transportation Safety Board chairwoman Jennifer Homendy has called an “all-hands-on-deck event”.
Investigators are examining the actions of the military pilot as well as air traffic control, after the helicopter apparently flew into the jet’s path.
Air crash investigations normally take 12-18 months, and investigators told reporters on Thursday that they would not speculate on the cause.
It has been suggested the helicopter exceeded an altitude limit.
Mr Trump said in a Friday morning post on his Truth Social platform that the helicopter was “flying too high” at the time of the crash.
“It was far above the 200 foot limit. That’s not really too complicated to understand, is it???” he said.
His comments came a day after he questioned the helicopter pilot’s actions while also blaming diversity initiatives for undermining air safety.
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Details have been emerging about others who died in the crash, including Danasia Elder, a flight attendant on the American Airlines flight, WSOC-TV in Charlotte, North Carolina, reported.