FCA Jeep chief Mike Manley has said software upgrades for 1.1m vehicles recalled for roll away risks, including the Grand Cherokee, will be available by the end of June 2016. Meanwhile, its Maserati unit is recalling cars in the US to fix a similar problem.
"We are going to be rolling out the recall (fix) before the end of this month," Manley said.
A 2015 Grand Cherokee was recently involved in the death of actor Anton Yelchin, a Reuters report noted .
The upgraded software includes an 'auto park' feature that eliminates the possibility of the driver inadvertently failing to place the transmission into park prior to exiting the vehicle, according to a document sent to dealers first reported by the automotive website Jalopnik.
Other electronically operated automatic transmission shifters, including those in BMW and Toyota Prius models, have a prominent 'P' button separated from the driving positions.
According to Reuters, Manley said FCAwas conducting a "thorough investigation" of the Yelchin incident but did not estimate when such a probe would be completed. Los Angeles police and US safety officials are also conducting their own investigations.
Manley said Jeep engineers want to inspect the 2015 Grand Cherokee involved in the death of Yelchin, who appeared in the movie Star Trek.
"We have not been able to but will as soon as possible carry out a full investigation. Until that stage, obviously, there's a huge amount of speculation of what may or may not have happened. I'm not entirely sure that's useful at this moment."
Yelchin was killed when his SUV rolled backward in the steep driveway of his Los Angeles home and pinned him against a brick wall and a fence.
The problem of vehicles rolling away when they are not supposed to compounded for FCA on Thursday when its Maserati brand recalled 13,092 Quattroporte and Ghibli luxury cars in the United States for issues similar to the Jeep recalls.
The Maserati models, US safety officials told Reuters, were recalled because they may roll away after drivers mistakenly believe they have engaged the vehicles in park.
In April, Fiat Chrysler recalled 1.1 million vehicles worldwide over the same issue.
FCA has not yet said if the Maserati recall covers vehicles outside the US.
The earlier recall was linked to 41 injuries, 212 crashes and 308 reports of property damage, and came after the National Highway Traffic Safety Administration (NHTSA) opened an investigation in August into the issue and upgraded the probe in February.
Maserati North America said in documents posted with NHTSA it was unaware of any injuries or crashes linked to the issue. It is investigating whether a software re-flash will fix the problem and hopes to have the update ready later this year.