FORT LAUDERDALE, Fla.—A U.S. transportation-safety agency said it would begin examining the fiery crash of a Tesla Inc. Model S car that killed two teenagers here Tuesday evening, marking the fourth active federal probe involving the company’s vehicles.

The National Transportation Safety Board said Wednesday it is initially focusing its latest investigation on the emergency response to the fire created by the electric car’s lithium-ion battery. The agency added that at this time it doesn’t anticipate Tesla’s driver-assistance...