The children first came to New York in the dark and some left that way, too. Others, after much confusion, did not leave at all.

As the federal government raced to meet a deadline on Thursday to reunite parents and children separated at the Southwest border, New York officials and lawyers for the children described the efforts as chaotic and contradictory, leaving many families still divided.

According to Gov. Andrew M. Cuomo, who spoke on a conference call on Thursday, some 80 youngsters were on a list to be released from Cayuga Centers, the child welfare agency that was caring for a large number of them, on Wednesday. More than a dozen white vans had lined up outside the East Harlem center in the evening, according to Telemundo. But the list turned out to be incorrect, Mr. Cuomo said, with many children on it not even in Cayuga’s care.

Cayuga later received a new list with only 14 names on it. Those children were then driven to La Guardia Airport for a flight departing after midnight. But when the children arrived at the airport, the Cayuga personnel discovered that only seven of them had been booked on the flight, according to the governor.