Federal auto safety regulators are investigating Cruise, following pedestrian injuries that involved the companies' driverless vehicles. The investigation is to determine whether Cruise automated driving systems "exercised appropriate caution around pedestrians in the roadway," a filing on the National Highway Traffic Safety Administration website .

NHTSA opened the probe into Cruise, a subsidiary of , on Monday. The probe was prompted by two reports involving pedestrian injuries and Cruise vehicles in recent months. The agency also cited two other incidents it identified through "videos posted to public websites," according to the filing.

The probe concerns an estimated 594 self-driving Cruise vehicles, according to the filing.

One incident on Oct. 2 where a pedestrian was thrown by another vehicle into the path of a driverless Cruise vehicle. That incident matches the in San Francisco, which resulted in one pedestrian being transported to the hospital.

At the time of the incident, the company said its autonomous vehicle braked "aggressively" and that it was "actively working" with San Francisco police to identify the hit-and-run driver. Cruise said it had spoken with the NHTSA about the Oct. 2 incident and provided it with video footage, adding that the regulator had not raised further questions.

The According to the incident report, a Cruise autonomous vehicle moving at a speed of about 1.4 miles per hour struck a pedestrian who stepped into a crosswalk after the stoplight had turned green, and the vehicle was allowed to proceed, according to the incident report. The pedestrian was then transported by emergency medical services. The company also said the pedestrian was transported after experiencing knee pain.

Cruise said the NHTSA had not spoken with the company about the August incident or the two incidents apparently posted on social media.

"Cruise's safety record over 5 million miles continues to outperform comparable human drivers at a time when pedestrian injuries and deaths are at an all-time high," Cruise spokesperson Hannah Lindow said in a statement to CNBC. "Cruise communicates regularly with NHTSA and has consistently cooperated with each of NHTSA's requests for information — whether associated with an investigation or not — and we plan to continue doing so."

The company, alongside subsidiary Waymo, has been deploying its vehicles . Critics of the autonomous driving rollout, including , have cited incidents where driverless vehicles have obstructed emergency vehicles.

Proponents have argued that driverless vehicles are safer than human-driven ones. , including some based in China, have also attained permits to test driverless vehicles on San Francisco streets.

— CNBC's Lora Kolodny contributed to this report.

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