The reactors are in Fukui Prefecture on the west side of the island of Honshu. Fukui Gov. Issei Nishikawa asked the prime minister to explain why the restart is necessary, the Kyodo News Service reported.
All of Japan's commercial reactors, which had been supplying about 30 percent of the nation's electricity, were shut down last year after the disaster at Fukushima. The Fukushima reactors were severely damaged by the Tohoku earthquake and the tsunami that followed.
Noda said the two reactors at Oi are disaster-proof, The Japan Times reported.
"We have established systems that ensure accidents won't occur," Noda said. "We have appropriate countermeasures in place. Even if the reactors lose their entire electricity supply, their cores won't suffer meltdowns."
Noda said that his government will take the opinion of local officials into account even though it is not legally necessary, Kyodo said.