The automaker says five fires were reported related to the defect. There have been no reports of injuries or deaths.
The recall announced Monday covers FJ Cruisers manufactured between October 2012 and January 2014.
Some 10,180 are in the Middle East and 2,500 in Australia; the rest were in Africa and Panama.
Monday's recall follows a bigger one last week covering 1.9 million Prius cars globally for a software problem and 294,000 vehicles - the RAV4 sport utility, Tacoma pickup and Lexus RX 350 luxury model - in North and South America for a different software glitch.