Maehara, who resigned as foreign minister in March, said he will focus on uniting the ruling Democratic Party of Japan and halt its plummeting approval ratings.
The DPJ fell out of favor due partly to a mishandling of the affairs in the aftermath of March's earthquake and tsunami disasters and the ensuing Fukushima nuclear plant crisis.
Maehara, 49, likely will face Finance Minister Yoshihiko Noda, Trade Minister Banri Kaieda and several other DPJ members in the contest.
He told members of his party that it must "change the government to give the people hope and a sense of security for the future," a report in The Japan Times said.
"We must follow policies that address people's concerns and give them a feeling of security and hope," Maehara said. "Please allow me to stand at the helm of our efforts to overcome the national crisis with the help of every single one of you."
Maehara briefly led the center-left DPJ in 2005 and resigned as Kan's foreign minister in March after receiving an illegal $3,000 political donation from a foreign national -- an ethnic Korean living in Japan, the BBC reported.
The winner of the party's internal election will be Japan's sixth prime minister in five years and be installed by next Tuesday.
Also expected to run will be Farm Minister Michihiko Kano, former Transport Minister Sumio Mabuchi and ex-Environment Minister Sakihito Ozawa.
But because time is short and there is a high number of candidates, serious policy debates may be lacking, Tomoaki Iwai, a political science professor at Nihon University, told the Times. Voters' main concern will be about who can unite the DPJ and work with the opposition parties.
"The whole point of the race is to replace Kan, who has been criticized for his lack of leadership and inability to work with the opposition," Iwai said. "The race will be about intra-party power balances. Tax hikes and other issues will be put on the back burner."
Despite mounting criticism of Kan, none of the DPJ candidates nor executives of the Liberal Democratic Party, the main opposition, has put forward any grand policy alternatives for rebuilding disaster-stricken Japan, Iwai said.
The crisis within the DPJ came to a head in early June when Kan announced he'd resign as soon as post-earthquake recovery plans were more concrete.
"I'd like to pass on my responsibility to a younger generation once we reach a certain stage in tackling the disaster and I've fulfilled my role," Kan said in a nationally televised meeting of DPJ members in June.
The DPJ and its allies hold 309 of the seats in the 480-member House of Representatives.
The current crisis for the DPJ arose when Kan, 64, was unable to agree with the center-right Liberal Democratic Party on how to rebuild the communities and infrastructure destroyed by the environmental disaster in March which left nearly 24,000 people dead or missing.
The DPJ -- which was formed in 1998 when several opposition groups joined forces -- came to power in 2009, ending the LDP's grip on power for all but 10 months since 1955.
Kan, himself, took office in wake of a previous DPJ crisis last year when Prime Minister Yukio Hatoyama resigned after he backtracked on a pledge to move a major U.S. military base from the island of Okinawa.