The safety group says it has received over 70 complaints about the modules and that the government has received hundreds.
A Chrysler spokesman said he is working on a response, and NHTSA said it is looking into the petition.
The center's petition said that Chrysler's "Totally Integrated Power Module," which includes a computer, relays and fuses, distributes electrical power through the entire vehicle. In addition to stalling, the faulty modules have may have caused air bags not to inflate and fuel pumps to keep running, causing unintended acceleration and fires, the petition said.
Clarence Ditlow, the center's executive director, said the modules are in about 7 million Chrysler vehicles. The company, he said, started phasing them out in 2012, but they remain in the 2014 Jeep Wrangler and the Dodge and Chrysler minivans.
Car owners and advocacy groups can petition the NHTSA asking for investigations that sometimes lead to recalls. The Center for Auto Safety has successfully petitioned NHTSA in the past, including one instance that led to the recent recall of 1.56 million older Jeep SUVs with fuel tanks mounted behind the rear axles. The center contended the tanks can leak fuel and cause fires in a crash, while Chrysler maintains the tanks perform as well as comparable models from other automakers.
In the past four years, NHTSA has been slow to act on most petitions. A review of the 15 petitions filed since 2010 by The Associated Press showed that in 12 cases, the agency took longer than the 120-day legal deadline to decide on an investigation.
NHTSA said the petitions often cover complex issues and the agency often needs more time to make a decision.