PARIS—Airbus Group SE on Tuesday followed rival aircraft maker Boeing Co. in reporting a nearly 29% drop in net commercial plane orders last year, though the European manufacturer played down concerns demand for new aircraft is softening.

Airbus said it booked 1,036 net commercial plane orders in 2015, from 1,456 a year earlier, but outselling Boeing which last week said it booked 768 net orders last year.

The...