After the software update on July 6, Cruise said it had gradually reintroduced unprotected left turns, which refers to turning left at an intersection with a solid green light that directs all traffic, rather than a designated green arrow just for turning vehicles.
Cruise emphasized in a statement Thursday all vehicles had software updates and the recall "does not impact or change our current on-road operations."
The company added "Cruise AVs are even better equipped to prevent this singular, exceptional event."
NHTSA said "an improper (Automated Driving Systems) response can increase the risk of a crash."
NHTSA said last month it opened a special investigation into the Cruise crash.
Cruise said NHTSA "suggested that the appropriate mechanism for disseminating this information" about the update was for Cruise to file a recall notice.
In rare circumstances, Cruise said the software caused the autonomous vehicle to hard brake while performing an unprotected left turn that it deemed necessary to avoid a severe front-end collision.
The self-driving vehicle "had to decide between two different risk scenarios and chose the one with the least potential for a serious collision at the time, before the oncoming vehicle’s sudden change of direction," Cruise said.
Cruise also noted a police report found the party most at fault for the June crash was the other vehicle, which was traveling at 40 miles per hour in a 25-mile zone.
In March, startup technology firm Pony.ai agreed to recall some versions of its autonomous driving system software, after an October crash in California, that had been used in three vehicles.
NHTSA said at the time it was the "first recall of an automated driving system."
In June, Cruise said it had started charging fares for driverless rides in San Francisco, after it became the first company to secure a permit to charge for self-driving car rides in the U.S. city, having overcome objections by local officials.