In a televised statement, Mr Kan warned of sweeping power cuts to come.
He said the situation at the quake-hit Fukushima nuclear plant remained grave, a day after an explosion at a reactor.
Meanwhile, police have warned that the death toll in tsunami-hit Miyagi prefecture alone could exceed 10,000.
Millions of survivors remain without electricity and authorities are stepping up relief efforts as the scale of the tragedy becomes clearer.
About 310,000 people have been evacuated to emergency shelters, many of them without power, Japanese broadcaster NHK reported.
Officials earlier announced that the number of troops helping with rescue work in the affected north-east region would be doubled to 100,000.
"The current situation of the earthquake, tsunami and the nuclear plants is in a way the most severe crisis in the past 65 years since World War II," Mr Kan said.
"Whether we Japanese can overcome this crisis depends on each of us.
"I strongly believe that we can get over this great earthquake and tsunami by joining together."
Mr Kan said the shutting down of the Fukushima plant and other power stations meant that electricity supplies were limited.
He said that from Monday there would be rotating stoppages of electricity that would also affect water and gas supplies and some medical facilities.
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