Machimura told Aljazeera he hoped for the release or medical treatment of Akihiko Saito, who has been missing since an ambush on Sunday by fighters in western Iraq.
"If an armed group is holding Mr Saito, we hope they will release him as soon as possible," Machimura said, according to a Foreign Mministry statement. "And as some information has it that he is injured, we hope he will be treated in a hospital."
Machimura also said Japan was committed to helping Iraq in its reconstruction.
An al-Qaida-linked group said it seized Saito, an employee of the British company Hart Security, in an attack on a convoy near Ramadi that killed 10 people. The firm said Saito may have died from his wounds.
"We have to do as much as possible for his release," Prime Minister Junichiro Koizumi said. "We have to ask for his release because Mr Saito has done nothing wrong."
Saito, who spent more than two decades in the French Foreign Legion, defied Japanese warnings not to enter Iraq for the lucrative job.
Saito is not linked to the 600 Japanese troops who are on a reconstruction mission in Iraq, the first time since the second world war that Japanese forces have been deployed to a country at war.
Japanese troops have a passive
role and are barred from combat
The troops, based in the relatively safe southern city of Samawa, have suffered no casualties and have not fired their weapons. Under Japan's pacifist constitution they are barred from combat except in the strictest definition of self-defence.
Five other Japanese have died in Iraq since the US-led invasion: two diplomats and two journalists killed in ambushes and a 24-year-old backpacker who was abducted and beheaded by fighters after Japan refused demands to pull out its troops.