Hong Kong CNN Business —  

Asian markets were mixed Tuesday as Chinese, Japanese and South Korean leaders met in China to talk about trade and politics.

Japan’s Nikkei 225 (N225) was slightly higher during a choppy session. China’s Shanghai Composite also rose 0.7%. But South Korea’s Kospi lost 0.6%.

Hong Kong’s Hang Seng (HSI) Index ended down 0.2% after a shortened trading session. The market closed early for the Christmas holiday and will reopen Friday.

The three Asia leaders agreed on Tuesday to continue talks about a free trade agreement among their countries while also pursuing a wider free trade pact in Asia Pacific — the Regional Comprehensive Economic Partnership.

The three sides also reaffirmed their commitment to denuclearizing North Korea, and support that country’s talks with the United States.

The meeting between three of Asia’s top executives happened at the close of a tense year, particularly for the relationship between Japan and South Korea. A trade spat between the two countries escalated into a military dispute over the summer. Seoul eventually said it would hold off on scrapping its military intelligence sharing agreement with Tokyo, lessening tensions somewhat. But trade remains an issue.

Tensions elsewhere on the Korean Peninsula were also in focus. Earlier this month, North Korea issued a veiled warning that it would send a “Christmas gift” to the United States, which a source familiar with the North Korean leadership said will likely be a new, hard-line approach in dealing with Washington.

On Monday, Chinese President Xi Jinping said in Beijing that he hopes to improve economic and trade ties with Japan and South Korea, according to the Chinese government.

Xi’s remarks came one day after China announced it will reduce import tariffs on hundreds of goods next week as it tries to boost trade and shore up its slowing economy.

Chinese Premier Li Keqiang also said Monday that Beijing is considering cutting reserve requirement ratios for banks in order to ease funding difficulties for small firms and increase economic growth.

— CNN’s Yoko Wakatsuki, Jake Kwon, Yong Xiong and Will Ripley contributed to this report.