"Japan is in the midst of reforms that must be carried forward," he said.
However, the ruling party's second-in-command, Secretary-General Hidenao Nakagawa, is resigning.
On Sunday, voters stripped the ruling Liberal Democratic Party and its junior coalition partner of their majority in parliament's 242-seat body upper chamber. The main opposition Democratic Party of Japan became the majority party in the upper house -- heralding an era of political deadlock with the Liberal Democratic Party, which remains in control of the lower house.
The Democratic Party of Japan was quick to assert its newfound clout, ridiculing Abe's decision to stay on as prime minister and questioning some of his policies.
"It's clear that the nation has given Mr. Abe a clear 'no.' How he can ignore that is absolutely baffling," Naoto Kan, the acting party chief, said in a televised debate. He spoke on behalf of party leader Ichiro Ozawa, who was recovering from a cold.
Another opposition party leader, Yukio Hatoyama, said the Democratic Party of Japan would oppose extending Japan's naval mission to support US-led operations in Afghanistan. The Japanese navy has provided fuel for coalition warships in the Indian Ocean since 2001; the current mission expires in November.
The Indian Ocean mission has been part of Tokyo's recent attempts to raise its international profile. Japan also sent noncombat troops to help rebuild southern Iraq.
The opposition party has criticized both operations, saying Japan's international efforts should be channeled through the United Nations, not the United States. Some within the party also say the missions violate the nation's pacifist constitution, which prohibits the use of force to solve international disputes.
Democratic Party of Japan officials also have criticized Abe over scandals in his Cabinet, including the alleged misuse of funds that has resulted in the departure of two ministers and is threatening a third.
The election was a dramatic reversal of the support Abe enjoyed when he took over from the popular Junichiro Koizumi less than a year ago.
Under Ozawa, the Democratic Party of Japan has made gains on a reform platform. Like the ruling party, Ozawa advocates an expanded role in international peacekeeping, but has criticized what he says is Abe's blind support of US foreign policy.
Still, the opposition would have to prove its mandate in elections in parliament's lower house, which Abe is not required to call for another two years. Yesterday, Abe rebuffed suggestions that he should call snap elections for the lower chamber.
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