UPDATE 2-Obama meets Myanmar PM, calls for Suu Kyi's release

* First meeting of a U.S. president with ASEAN

* Relative neglect has given China opening - analysts

* Obama shakes hands with Myanmar prime minister

* Joint statement urges "fair, inclusive" polls (Updates with meeting)

By Patricia Zengerle and Bill Tarrant

SINGAPORE, Nov 15 (Reuters) - U.S. President Barack Obama called for the release of Myanmar opposition leader Aung San Suu Kyi when he met the country's prime minister at a meeting with other Southeast Asian leaders in Singapore on Sunday.

Obama shook hands with Myanmar Prime Minister Thein Sein at the meeting in Singapore's Shangri-la hotel with the 10 leaders of the Association of Southeast Asian Nations (ASEAN), the first ever with a U.S. president.

The United States has begun to re-engage with Southeast Asia after years of relative neglect that left China to increase its diplomatic and economic heft in the region.

Speaking to reporters after the meeting, Obama said he reiterated his offer to Myanmar of better ties with Washington if it pursued democratic reform and freed political prisoners, including opposition leader Aung San Suu Kyi.