Toyota is recalling 1.5 million vehicles in Japan, 670,000 vehicles in the United States and 496,000 vehicles in Europe over a problem in the steering intermediate extension shafts, which could be damaged at slow speed, a spokesman said.
The problem, in cars such as the second-generation Prius and certain Corolla models can be fixed in under an hour.
Separately, Toyota is also recalling 630,000 vehicles worldwide, including 350,000 in the United States and 175,000 in Japan, to fix water pumps in hybrid vehicles, Tachikawa said.
Some vehicles are target of both recalls, making the total number of vehicles to be recalled at 2.77 million, he said.
Toyota has sold about 3.3 million Prius hybrid vehicles globally since the car went on sale in December 1997.
More top news
US singer John Legend said he was "moved" by footage of the teenager singing one of his songs.
John Noakes was Blue Peter's longest-serving presenter.
MI5 has reportedly launched two urgent inquiries into how it missed the danger posed by the Manchester bomber, Salman Abedi.