Abe called the next election a "historic battle" with strong confidences of leading the LDP return to power after the lost to DPJ in 2009.
The former Tokyo Governor Shintaro Ishihara, known for his strong nationalistic views, launched a new party named Sunrise Party on Tuesday, aiming to form a "third force" that could challenge the DPJ and the LDP in the House of Representatives election next month.
Ishihara has talked with leaders of two smaller parties in recent days to discuss political cooperation.
"I think I could dissolve the lower house Friday if LDP President Shinzo Abe makes promises on cutting the number of lawmakers in the 480-seat lower house," Noda said on Thursday during a parliamentary debate with main opposition LDP.
Abe said that the LDP would like to cooperate with Noda's Democratic Party of Japan on issuing the electoral system reform bill after the debate.
Japan's parliament passed key bills Friday on electoral system reform and government debt issuance, so that Noda have no reasons to delay the dissolution.
The election campaigning would commence on Dec. 4.
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