In a teary news conference on Friday night, Kosako said he could not stay on while the government set, what he deemed, inappropriate radiation limits for elementary schools near the plant.
"I cannot allow this as a scholar," he said, adding that he also opposed the government raising the limit for radiation exposure for workers at the plant.
The government has set 20-millisievert limit for radiation exposure as safe, but according to Kosako, that is 20 times too high, especially for children, who are considered more vulnerable to radiation than adults.
Plant workers are now allowed to be exposed to 250 millisieverts of radiation over a five-year period, up from 100 millisieverts.
Tokyo Electric Power Co., the utility that runs Fukushima Daiichi, revealed Saturday that the radiation exposures for two workers have been found to have reached the limit of 250 millisieverts.
Kosako went on to criticize the lack of transparency in Kan's government in dealing with the radiation leak and blasted it for not taking long-term action.
"I cannot help but to think [the government and other agencies] are only taking stopgap measures."
In a statement, Kan's administraton called the resignation "unfortunate," reiterating that the government "has consistently followed the advice of the nuclear safety commission in addition to the opinions from relevant sources."
The resignation is a major blow to the government. A Kyodo News service poll released Saturday showed that Kan's support ratings were plunging.
The poll reported 76 per cent of the respondents think Kan is not exercising sufficient leadership in handling the country's multiple crises.
Almost every day there are protests in Japan against the use of nuclear power.
About 1,000 protesters gathered Saturday in Tokyo's Yoyogi Park, chanting "No more nukes" and holding banners that read "Electricity in Tokyo, sacrifice in Fukushima."
More than 150,000 people have been forced to leave their homes in northeastern Japan due to the tsunami and nuclear catastrophe.
With files from The Associated Press