Chrysler Group LLC CEO Sergio Marchionne met with the nation’s top auto safety regulator last week about the government’s ongoing investigation into the Auburn Hills automaker’s Jeep SUV fix and other issues.

Marchionne met for 20 minutes on Wednesday — when he was in Washington on a visit for an unrelated meeting — with National Highway Traffic Safety Administrator David Strickland on a variety of topics, including the SUV fire probe and Chrysler’s support for future in-vehicle technology that could prevent drunken drivers from starting vehicles.

But nearly three months after NHTSA formally asked Chrysler to recall 2.7 million older Jeep SUVs for fire risks, the government’s investigation — opened in August 2010 — shows no signs of wrapping up.

Strickland disclosed Monday in a speech before the Governors Highway Safety Association that he had met last week with Marchionne, according to a copy of his prepared remarks obtained by The Detroit News. Chrysler declined to comment.

After negotiations that included talks between then-Transportation Secretary Ray LaHood and Marchionne, Chrysler agreed on June 18 to recall 1.56 million 1992-98 Grand Cherokees and 2002-07 Libertys. Under the agreement, Chrysler will install protective trailer hitches. NHTSA says the gas tank can rupture and catch fire when the Jeeps are hit from behind. NHTSA cites reports of 51 deaths in rear-end accidents in which older Jeep gas tanks leaked and caught fire.

Chrysler also will conduct a service campaign for about 1.2 million 1999-2004 Grand Cherokees that includes replacing aftermarket trailer hitches, but not installing them on vehicles without them. NHTSA had originally asked Chrysler to recall all 2.7 million Jeeps. Strickland says it hasn’t decided whether it will crash-test the remedy that Chrysler has proposed, as auto safety advocates have urged.