(Reuters) - U.S. safety regulators have opened an investigation into whether General Motors Co (GM.N) reacted fast enough in its recall of more than 1.6 million cars over an ignition-switch defect linked to 13 deaths in crashes.

The issue could prove costly to GM as the automaker faces a potential fine from the U.S. National Highway Traffic Safety Administration, the cost of replacing the ignition switches in question and the possibility of costly lawsuits.

"The National Highway Traffic Safety Administration has opened an investigation into the timeliness of General Motors' recall of faulty ignition switches to determine whether GM properly followed the legal processes and requirements for reporting recalls," the safety agency said in a statement released on Wednesday.

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GM previously said the weight on the key ring, road conditions or some other jarring event may cause the ignition switch to move out of the "run" position, turning off the engine and most of the car's electrical components.

NHTSA urged owners to follow GM's recommendation to "use only the ignition key with nothing else on the key ring" when operating the vehicle and seek the repair as soon as replacement parts become available. GM said the initial replacement parts will be available in early April.

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It previously said it is working with suppliers to increase production of replacement parts. GM said the ignition switch torque performance may not meet company specifications. The involved parts were made in Mexico, according to documents previously filed with NHTSA.