Tesla Model S is displayed inside of the new Tesla flagship facility on August 10, 2016 in San Francisco, California.

The U.S. National Highway Traffic Safety Administration said, after market close on New Year's Eve, that it plans a probe of a fatal Tesla crash that occurred on Sunday in Los Angeles.

The Los Angeles Police Department confirmed that a motorist in a black 2016 Model S ran a red light and struck a 2006 Honda Civic on Sunday, killing the two people in that car. The two occupants inside the Tesla were taken to a nearby hospital with non-life threatening injuries.

It was not immediately known whether Tesla Autopilot — the company's advanced driver assistance systems — may have been engaged at the time of the fatal crash, and if so, whether it might have caused or exacerbated the incident.

NHTSA, which is part of the Department of Transportation, has the power to issue mandatory vehicle recalls if it deems them necessary, typically when an automaker has failed to determine and fix dangerous flaws in their vehicles or parts, systems and components within.

The agency said, in a statement e-mailed to CNBC on Tuesday: "NHTSA's special crash investigation (SCI) program will initiate a crash scene and vehicle inspection of the 12/29/2019 crash of a Tesla Model S after it collided with another car in Los Angeles, California."

Tesla did not reply to a request for comment.

That same NHTSA program had previously initiated probes of 13 incidents or accidents involving Tesla electric vehicles with Autopilot possibly in use. Results of eleven of those investigations were still pending as of Tuesday.