The promise to hand over power to a younger generation mollified internal party rebels who had threatened to bring down Kan, the country's fifth premier in as many years, days before his first anniversary in the job.
The motion, brought by the opposition conservative Liberal Democratic Party (LDP) and
two small parties, was defeated by a margin of 152 against 293 after most lawmakers of the centre-left ruling party fell into line behind Kan.
In a last-minute appeal to his fractured Democratic Party of Japan (DPJ), Kan urged its lawmakers to stick together until his government makes significant progress in rebuilding after Japan's worst post-war emergency.
Kan offered no precise deadline, leaving his departure date open to interpretation.
The government has promised that most of the 100,000 people still living in shelters since the disaster will be in temporary housing by mid-summer, but wider reconstruction efforts are expected to take years.
The operator of the tsunami-hit Fukushima nuclear power plant has said it hopes to bring its six reactors to "cold shutdown" by October-January, but decommissioning and decontaminating the site will take far longer.
The opposition LDP, which was ousted in a landslide 2009 election after more than half a century of almost unbroken rule, tabled the no-confidence motion late on Wednesday along with two small parties.
LDP leaders have accused Kan of bungling the response to the disaster that left more than 23,000 dead and missing and sparked the world's worst nuclear crisis since Chernobyl a quarter-century ago.