Asked what Japan would do if Peru sought Mr Fujimori's extradition, Mr Fukuda said: "I believe the government will deal with the issue in accordance with Japan's domestic law."
The announcement raises the prospect of a diplomatic row, as Japanese law does not allow the extradition of Japanese nationals.
Peruvian legislators reacted angrily to the news and some said they felt betrayed by Japan.
Congresswoman Ana Elena Townsend said the Japanese government should not play into Mr Fujimori's hands by helping him avoid an investigation into his dealings.
Slush fund probe
Mr Fujimori, the son of Japanese emigrants to Peru, is the subject of a congressional investigation there into the activities of his former intelligence chief, Vladimiro Montesinos.
Investigators in Lima have said they will make all possible efforts to force Mr Fujimori to face questioning over alleged slush funds controlled by Mr Montesinos.
But Mr Fujimori has repeatedly ruled out returning to Peru, saying he does not believe he would receive a fair hearing from political opponents.
Correspondents say the Japanese decision will infuriate Peruvians, and raise question marks over the legitimacy of Mr Fujimori's entire 10-year presidency.
Ancestors
As a Japanese citizen, Mr Fujimori would not have been eligible to stand for the office despite having been born in Peru, and having grown up there.
According to the Yomiuri Shimbun newspaper, the government had agreed on three facts confirming Mr Fujimori's citizenship.
- His ancestors were registered in Kumamoto prefecture on Kyushu island, southern Japan
- He had taken no steps to renounce his Japanese nationality
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Peruvian law had allowed his parents to retain their Japanese citizenship
"The government has confirmed his Japanese citizenship after probing several points," the report added.