Kan said he was sorry for the mix-up, the BBC reported Friday.
"My instruction was inadequate and came too late," he said.
Two-thirds of Japan's nuclear reactors have remained inactive since a 9-magnitude earthquake and tsunami March 11 that killed more than 14,000 people.
The quake and tsunami heavily damaged the Fukushima Daiichi nuclear plant, causing fires and radiation leaks and forced a national review of the safety of power plants in the country.
The review last month found the plants safe to reopen so Kan's call Wednesday for "stress tests" on them came as a surprise.
The government needs to be clearer, said Kan's chief Cabinet secretary, Yukio Edano.
"We realize that we need to clarify the situation but right now we are discussing exactly what the next step will be," Edano said.
Complicating matters for Kan is the resignation of Ryu Matsumoto from the post of state minister for reconstruction measures, the Yomiuri Shimbun reported.
"The administration's governing ability has been paralyzed," said a member of the Democratic Party of Japan.