The Yomiuri Shimbun said its survey of 34 government leaders -- 13 governors and 21 heads of municipalities -- also found five of the leaders opposed restarting reactors and 23 declined to give their opinion on whether reactors should be restarted.
Japan shut down its last operating nuclear reactor this month.
Before the Fukushima plant was heavily damaged in last year's earthquake and tsunami, 54 commercial nuclear reactors were operating in Japan and they provided about a third of the country's energy supply.
Many of the undecided leaders told the Yomiuri Shimbun they would decide on whether to restart reactors based on the position of the central government and local residents on whether to restart the Nos. 3 and 4 reactors at the Oi nuclear power plant in Fukui Prefecture.
In April, the central government's safety standards were established to prepare for restart of the Oi reactors.
The mayor of Mihama town in Fukui Prefecture, along with the heads of Tomari village in Hokkaido and Kariwa village in Niigata Prefecture, told The Yomiuri Shimbun they "would approve [restarts] soon" after the reactors meet safety standards.
The mayor of Tomioka town in Fukushima Prefecture and the head of Tokai village in Ibaraki Prefecture said they would "unconditionally" reject the restart of nuclear reactors.
Critics have complained the Japanese government hasn't done enough to improve nuclear safety standards and point to close relationships between the government and the nuclear industry.
The lack of nuclear power has led to concerns about a summer energy shortage.
Notable deaths of 2014 [PHOTOS]
Syrian Al Qaida group executes Lebanese soldier