Washington (AFP) - A US vehicle safety agency has opened an investigation into a million Dodge SUVs and Ram pickup trucks that reportedly continued to move even when in park, causing nine injuries.

There have been 25 crashes reported of the 34 incidents of the cars moving when drivers shifted into park, the National Highway Traffic Safety Administration (NHTSA) confirmed Tuesday.

The investigation into the Fiat Chrysler Automobile models is another hit to the company after "Star Trek" actor Anton Yelchin was killed in June when his 2015 Grand Cherokee rolled down his driveway, slamming him into a wall.

Fiat Chrysler had recalled that model in April after reports of 117 crashes and 28 injuries, involving drivers who said the car moved even after they thought it was locked in park.

The latest NHTSA investigation covers 2013-2016 Ram 1500 trucks and 2014-2016 Dodge Durango's SUVs, and covers incidents where vehicles were turned off as well as with the engine running.

"A preliminary evaluation has been opened to assess the scope, frequency, and safety-related consequences of the alleged defect," NHTSA said in the notification.

"Notably none of the reports indicate that the parking brake was engaged at the time of the roll-away incident."

Fiat Chrysler said it is "cooperating fully" with the investigators, and said the scope was limited as other models with similar shift mechanisms were not included.

The shift mechanism for the Dodge and Ram models is different from the Grand Cherokee models involved in the April recall, which was found to be confusing to some drivers.

The agency opened an investigation into similar rollaway problems reported in 2012-2014 Land Rover Evoque SUV and the 2013 Jaguar XF luxury sedan. Four complaints and one injury were reported in the incidents, none of which had the parking brake engaged.