The five candidates have spent the weekend jockeying for position with fellow MPs In the first round, no candidate secured enough support and a run-off vote is now under way between Mr Kaieda and Finance Minister Yoshihiko Noda.
Correspondents say the winner will face a daunting agenda.
Large parts of Japan need to be rebuilt after March's earthquake and tsunami, and the crisis at the crippled Fukushima nuclear power plant still needs to be resolved. Added to that, the new prime minister will need to address Japan's stagnant economy.
Mr Kan stepped down after just 14 months in charge.
He was criticised for failing to show leadership after the earthquake and ensuing nuclear crisis.
After the 398 MPs of the ruling Democratic Party of Japan (DPJ) conclude their vote, the winner will become prime minister once approval is given by the Diet, or parliament.
In the first round, Mr Kaieda gained 143 votes and Mr Noda 102. Many supporters of third-placed former Foreign Minister Seiji Maehara, who won 74 votes, were expected to back Mr Noda.
The five candidates spent the weekend jockeying for position among DPJ MPs.
The contest has turned into a bitter factional battle between supporters and enemies of the powerful, but scandal-tainted kingmaker, Ichiro Ozawa.
He has thrown his support behind Mr Kaieda.
Mr Ozawa is believed to command the loyalty of about 130 members of the Diet, despite awaiting trial on charges of misreporting political donations.
Known as the Shadow Shogun for his backroom power, he has been suspended from the party, a decision Mr Kaieda has hinted he may review, the BBC's Roland Buerk in Toyko reports.
The favourite with the public was Mr Maehara, who would have become Japan's youngest leader since World War II if elected.
Farm Minister Michihiko Kano and former Transport Minister Sumio Mabuchi were also in the contest.
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