WASHINGTON (Reuters) - The leading U.S. rail regulator on Thursday ordered Amtrak to take immediate steps to improve the safety of its busiest route, formalizing a request that the company made days after a deadline derailment in Philadelphia.

The Federal Railroad Administration ordered Amtrak to identify dangerous curves along the Northeast Corridor between Washington and Boston where slower speeds could reduce the risk of mishap.

Amtrak, the nation's leading passenger service, must then activate controls that would slow down a runaway train and otherwise control the speed, according to the FRA order.

"Amtrak must identify other actions it will take to ensure compliance with speed reductions," according to the order.

Last week, an Amtrak derailment in Philadelphia killed eight passengers and sent more than 200 to local hospitals.

The system FRA wants in place is called automatic train control (ATC), which detects when a train is traveling above the speed limit, sending a signal to the engineer. If the operator fails to act, the system will automatically apply the brakes.

A more advanced system, called positive train control (PTC), is due to be in force by the end of the year and Amtrak has said it expects to achieve that deadline.

(Reporting by Patrick Rucker and David Morgan; Editing by Richard Chang)