The contest comes half a year after Japan was hit by the devastating quake, tsunami and nuclear disasters and two years after the Democratic Party of Japan (DPJ) ousted the long-ruling conservative party in a landslide.
Kan announced his resignation after just 15 turbulent months in office during which his leadership style, his response to the March 11 calamity and his outspoken anti-nuclear stance earned him critics and enemies.
The winner of Monday's vote, to be confirmed by parliament as premier the next day, must tackle problems from rebuilding the disaster zone and ending the Fukushima crisis to reviving a stagnant economy and reducing huge public debt.
Japan's sixth new premier in five years must also manage tricky relations with China, the traditional rival that last year overtook Japan as Asia's biggest economy, as bitter territorial disputes are simmering.
The new leader will also face the same problems that have hobbled his two short-lived DPJ predecessors -- deep rifts within the ruling camp and a hostile opposition that controls the upper house of parliament.
Among the leading candidates, the youthful and conservative-leaning ex-foreign minister Seiji Maehara, 49, became the favourite of pundits and in public opinion polls when he declared his candidacy last week.
Maehara backs a strong US alliance and has taken a hard line on China, last year infuriating Beijing by labelling its stance in an island dispute as "hysterical".
He resigned five months ago for taking political donations from a family friend who is an ethnic Korean, in contravention of funding laws, a fact the opposition is likely to again seize upon.
Another strong contender is Trade and Industry minister Banri Kaieda, 62, an economist backed by controversial party kingmaker Ichiro Ozawa, who controls the biggest faction among the 398 DPJ lawmakers in Monday's vote.
Ozawa, who has been dubbed the "Shadow Shogun" and faces criminal charges over a donations scandal, commands the support of some 130 lawmakers, despite the fact that he lost his party membership following his indictment.
Another candidate is Finance Minister Yoshihiko Noda, 54, who has led Japan's mixed efforts to bring down the yen, a "safe haven" currency that has soared to post-war highs amid global market turmoil, hurting Japan's exporters.
Noda, seen as a safe pair of hands, has managed to upset Japan's neighbours, including South Korea, with comments defending Japanese war criminals.
Like previous internal DPJ contests, the ballot outcome is likely to be determined as much by factional deal-making as by the candidates' popular appeal and policy positions.
One key question is how to cut a debt mountain that has ballooned to twice the size of the five-trillion-dollar economy and is set to grow more as Japan spends billions of dollars on quake reconstruction.
The problem is acute for Japan, with one of the lowest birth rates and highest life expectancies on earth, as tax revenues are set to fall and social welfare bills rise in coming decades.
Noda has advocated raising the sales tax, although he recently eased off that politically risky position. Maehara has warned that a tax hike now would worsen chronic deflation and could snuff out a post-quake recovery.
Also looming large is Japan's energy policy after the quake-prone country suffered the world's worst nuclear accident since Chernobyl 25 years ago, which forced mass evacuations and contaminated a wide swath of farm land.
Kan advocated a nuclear phase-out and made his resignation conditional on passing a law promoting renewable energy, but his prospective replacements have sounded a more cautious note.
"The top priority for the new prime minister is reconstruction from the disaster," said Shinichi Nishikawa, politics professor at Meiji University.
The new leader will also have to mend ties with the opposition and rebuild the DPJ itself, which remains under Ozawa's influence, he told AFP.
"Extremely tough jobs await the next prime minister," Nishikawa said. "It's like pulling chestnuts out of the fire."