Tesla Inc. said new-vehicle deliveries in the first quarter fell 31% from the previous three months as the electric-car maker struggled to ship its Model 3 compact car to customers in Europe and China for the first time.

The Silicon Valley auto maker Wednesday said it delivered about 63,000 vehicles in the latest period, worse than analysts’ already-lowered expectations. Analysts on average had predicted deliveries would drop to 73,500, according to FactSet, a figure reflecting total deliveries of Model 3, Model S and Model...