Volkswagen Group offered to buy the rest of Navistar International Corp. for about $2.9 billion, a deal that would address the German manufacturer’s absence from the U.S. heavy-truck market, according to people familiar with the matter.

VW’s Traton SE unit has offered Navistar holders $35 a share in cash, according to a statement, confirming a Bloomberg report. Traton already owns a 17 percent stake in Navistar, whose biggest holder is billionaire investor Carl Icahn, according to data compiled by Bloomberg.

Navistar shares soared as much as 51 percent to $36.35 in late trading Thursday. The Lisle, Ill., company builds International-brand trucks, school buses, defense vehicles and engines.

VW’s heavy-truck division has for years tried to reduce its reliance on Europe and South America to become a global competitor to industry leaders Daimler and Volvo AB. Traton CEO Andreas Renschler had hinted at potential interest in boosting VW’s stake in Navistar in the past, but the company mainly focused on alliances rather than acquisitions to build scale.

VW acquired its stake in Navistar two years ago, laying the groundwork for a footprint in the North American market, the truck industry’s largest source of profits. Daimler’s Freightliner and Volvo’s Mack divisions generate significant sales in the region.

Acquiring Navistar could be a way for VW to save money as auto and heavy-truck makers prepare for a downturn after years of growth. Navistar, truck-engine maker Cummins Inc. and supplier Meritor Inc. announced thousands of job cuts late last year.