TOKYO (Reuters) -- Japanese Prime Minister Junichiro Koizumi, in what was likely to be his last speech to Parliament as premier, vowed on Friday to forge ahead to mend fences with two key Asian neighbors, China and South Korea.

Japan's ties with the two countries have chilled markedly since Koizumi took office in 2001 and began annual visits to a shrine where war criminals convicted by an Allied tribunal are honored along with Japan's 2.5 million war dead.

Japan's diplomacy toward the rest of Asia is expected to be a key policy issue in the race to head the ruling Liberal Democratic Party (LDP) after Koizumi's term as party president ends in September.

"Although there are differences of opinion and confrontations over some issues, China and South Korea are our important neighbors and we will ... build future-oriented relations based on mutual understanding and trust," Koizumi said in a keynote address to a new session of Parliament that began on Friday.

Koizumi made no mention in his speech of his pilgrimages to Tokyo's Yasukuni shrine, seen by critics as a symbol of Japan's past militarism. Koizumi has repeatedly stressed that he visits the shrine to pray for peace.

Foreign Minister Taro Aso, a possible contender to succeed Koizumi, echoed the prime minister's views on Asian diplomacy in a separate speech to Parliament on Friday.

"Developing Sino-Japanese relations is one of our country's basic foreign policies," Aso said.

"With reconciliation and cooperation as a guiding spirit, we must draw a bright picture of our future relations with China and South Korea by deepening dialogue," he said.

Chief Cabinet Secretary Shinzo Abe, the front-runner to succeed Koizumi as prime minister in public opinion polls, said this week that Japan's foreign policy on Asia would be a focal point of the campaign.

Abe, known for his hardline stance towards China and North Korea, argued that while Tokyo's ties with Beijing and Seoul were strained, Japan should forge stronger relations with India and Australia to secure Japan's presence in the region.

Other possible candidates to succeed Koizumi include former Chief Cabinet Secretary Yasuo Fukuda and former LDP executive Taku Yamasaki, who are critical of Koizumi's Asian diplomacy.

Finance Minister Sadakazu Tanigaki is also seen as a contender, but he tends to steer clear of emphasizing Asian diplomacy as a key issue.

Koizumi, who came to power in April 2001 promising to revitalize the economy through reform, is the longest-serving prime minister since former prime minister Yasuhiro Nakasone, who served from 1982 to 1987.