Ten people were taken into custody yesterday at Kennedy International and La Guardia Airports shortly after they were reopened for the first time since the terrorist attacks on Tuesday. The authorities then abruptly shut all three major New York-area airports again.

Law enforcement officials said one of those held was carrying a false pilot's identification. And at least one of them had tried on Tuesday while wearing an American Airlines crew uniform to board a flight to Los Angeles around the time of the hijackings, only to become infuriated when it was canceled because of the attacks at the World Trade Center.

Several of those detained yesterday showed up at the airport with tickets for flights canceled on Tuesday and tried to use them, officials said. The man with the false pilot's identification was arrested, and he and the others were being questioned to determine whether they were part of a plot to attack American targets.

''There has been one arrest made by the Port Authority Police Department at a New York airport,'' Barry W. Mawn, the head of the New York F.B.I. office, said through a spokesman. ''There are also three other instances at the airports in which the F.B.I. and Joint Terrorist Task Force are conducting an investigation.''