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But his ruling party also pledged the same day to push for changes to Japan's pacifist constitution -- a move likely to stir unease in both the countries, which were among victims of Tokyo's 20th century militarism.
"I am in the same generation as the two new leaders," Abe told an annual convention of his Liberal Democratic Party (LDP), referring to Chinese President Xi Jinping, 59, and South Korean President Park Geun-Hye, 61.
The 58-year-old Abe became prime minister in December for a second time when his conservative party secured a landslide election victory, while Tokyo was locked in disputes with Beijing and Seoul over island chains.
"For prosperity and stability in the region, it is necessary for the three of us to build mutual understanding," Abe told the convention.
"I want to say that Japan's door is always open toward China," said Abe, who was previously premier from 2006-2007.
But earlier in the day, the premier urged graduates of the National Defence Academy to guard the country against "provocations", an apparent reference to the row with Beijing over sovereignty of a Tokyo-controlled island chain.
Chinese ships have routinely circled the Senkaku islands, which Beijing claims as the Diaoyus, since Tokyo nationalised some of them in September.
Abe, in his speech to graduates, emphasised that the security situation had changed since they started their course four years ago.
"Unlike four years ago... provocations are continuing against our country's territorial land, sea and air," he told the graduation ceremony.
"What is happening in the field where you will be is a harsh reality and a crisis that is there," he added.
"I wish you to dedicate yourselves to noble duty in the field, to defend the people and the country."
The LDP convention adopted a wide-ranging action plan, including efforts to create an "independent constitution" to replace the US-imposed post-war charter which bans the use of force in settling international disputes.
The ban limits the so-called Self-Defence Forces to a strictly defensive role and bars them from taking aggressive action.
The hawkish Abe has said Japan must redefine its rules of engagement to provide an effective deterrent against North Korea and balance China's growing military might.
Abe said in January he intends to change the constitution, by modifying an article which stipulates that amendments need a two-thirds majority in parliament.
The LDP and its junior coalition partner New Komeito have a more-than two-thirds majority in the lower house, but New Komeito and some LDP factions are cautious about amendments.
The less powerful upper house is controlled by no single party, but the opposition Democratic Party of Japan has the greatest number of seats.
Elections for half the upper house seats must be held around July.
"We will definitely win through the (upper house) election and reestablish a proud Japan," Abe told the convention.
The party action plan also reaffirmed Japan's intention to join the US-led Trans-Pacific Partnership free trade talks, despite persistent objections from farmers and others.
It said Japan will negotiate "in a manner which will protect national interests including the agriculture and fishery sector".
"I will definitely protect Japan's agriculture and food. I want you to trust me," Abe said.