The recall involves 2004-2005 and 2007-2009 model year minivans that have defective shift lever assemblies, The Detroit News reported. The shift levers could be moved out of park without the foot on the brake pedal, which "could result in a vehicle rollaway," Toyota said.
Twenty-one minor accidents that included two minor injuries have been reported, the company said.
The Toyota recall covers 615,000 vehicles in the United States, 56,000 in Canada and 23,000 in Mexico.
Also Thursday Hyundai Motor Co. recalled 760,000 vehicles in North America because of brake light issues, while Nissan Motor Co. recalled 908,900 vehicles -- most of those in Japan -- because of faulty sensors that could cause vehicles to stall, the newspaper said.
The Hyundai recall covers the following models: 2006-2007 Accent, 2009-2011 Elantra Touring, 2007-2008 Entourage, 2009-2011 Genesis, 2007-2010 Sonata, 2006-2008 Tiburon, 2009-2011 Veracruz and 2006-2007 and 2009-2011 Tucson, as well as the 2007-2011 Kia Azera.
Nissan's recall affects the Infiniti M, X-trail sport utility vehicle and Serena minivan models sold mostly in Japan.