Hitachi has also enlisted the help of overseas firms including General Electric Co GE in its bid to win the decommissioning order, while Toshiba is being aided by Babcock & Wilcox Co and Shaw Group Inc.
Hitachi and Mitsubishi Heavy, which already have business ties, said they are looking at ways to work together to help improve conditions at the plant and aid operator Tokyo Electric Power Co and the government.
Radiation leaks from the northern Japan plant, which was severely damaged by the massive earthquake and tsunami on March 11, have made it the world's worst nuclear crisis since the Chernobyl disaster 25 years ago.
Toshiba manufactured two of the Fukushima Daiichi reactors by itself and two jointly with GE. Hitachi manufactured another, with a sixth supplied by GE.