Japan Prime Minister urges nuclear-free future
In a televised news conference, Mr Kan said the country should harness renewable energy sources.
The 11 March earthquake and tsunami wrecked the Fukushima plant, which continues to leak radioactive material.
A large section of public opinion has turned against nuclear power.
About 30% of Japan's electricity was nuclear generated before the Fukushima crisis, and the country had targeted raising that figure to 53% by 2030.
But Mr Kan had already said this commitment should be scrapped.
On Wednesday, he went a step further, saying: "We will aim at realising a society which can exist without nuclear power."
He said the country should aim to develop alternative energy sources such as solar, wind and biomass.
But he did not lay out a timescale for his plan.
Last month Mr Kan headed off a bid to topple him from power by telling his colleagues he would step down when Japan's crises were under control.
But his continued refusal to say when he will quit has led to speculation that he might call a snap election on the nuclear issue.
In Wednesday's news conference, he denied that he intended to call an election
Mr Kan has slumped to his lowest level of popularity since he took office just over a year ago.
According to an opinion poll this week, just 16% of the population believe he is doing a good job.