The crash between an Air Canada Express jet and a fire truck at LaGuardia injured dozens of passengers and led to hundreds of flight cancellations.
The crashed jet remained visible at the airport on Monday, its crushed cockpit pointing skyward.
The two young pilots who died in the incident had just started their careers, said Bryan Bedford, head of the Federal Aviation Administration. "It's an absolute tragedy," he said at a news conference.
On Monday, US Immigration and Customs Enforcement agents with bulletproof vests and pistols were taken off the streets and redeployed in airports in Atlanta, New York and New Jersey, according to Reuters witnesses.
Trump said they were being sent to airports to help TSA agents reduce security screening lines, over the objections of the TSA workers' labour union, who said ICE agents had not undergone the months of airport security training needed.
White House immigration czar Tom Homan said agents had been deployed to 14 airports, in cities including New York, Chicago, Atlanta and Houston.
Authorities said the agents would provide crowd control, but Trump said they could also make arrests - raising concerns that the chaotic raids that have played out on the streets of Minneapolis, Chicago and elsewhere might come to the nation's airports as well.
"They're able to now arrest illegals as they come into the country. That's very fertile territory," Trump told reporters. "But that's not why they're there. They're really there to help."
In New York, the pilot and first officer of an Air Canada Express jet were killed when the plane collided with a fire truck while taxiing. Another nine people were hospitalised with serious injuries.
The CRJ-900 plane, operated by regional partner Jazz Aviation, had been carrying 72 passengers and four crew members.
Some 572 flights were cancelled, more than 50 per cent of LaGuardia's daily total. Some flights resumed on Monday afternoon, but the FAA said the runway where the accident took place would be closed until Friday, which will likely cause delays throughout the week.
US aviation has faced a chronic shortage of air traffic controllers, but US Transportation Secretary Sean Duffy said that was not a problem at LaGuardia. "It's a very well-staffed airport," he said at a news briefing.
Kathryn Garcia, executive director of the Port Authority of New York and New Jersey, said earlier in the day that the fire truck was responding to a separate aircraft that had reported an "issue with odour."
According to air traffic control audio, a controller can be heard telling the craft that a fire truck was en route and clearing a truck to cross a runway. Moments later, the controller can be heard saying: "Stop, stop, stop, truck 1 stop, truck 1, stop."
