MANILA — Secretary of State Rex W. Tillerson will for the first time on Sunday be in the same room with his North Korean counterpart, and much of the world will be watching for whether the two even acknowledge each other.

Joining them in Manila will be representatives of other countries with a stake in the regional confrontation, including China, Russia, South Korea and Japan. The occasion is the annual ministerial meeting of the Association of Southeast Asian Nations, or Asean, which will be followed later this year by a meeting of the leaders of the organization’s nations. President Trump has promised to attend that meeting.

Mr. Tillerson and North Korea’s foreign minister, Ri Yong-ho, are this year’s most intriguing pairing, and their diplomatic choreography — whether they avoid each other or sit down together — could set the course for the Trump administration’s moves on its top foreign policy priority for the rest of the year.

State Department officials said Mr. Tillerson and Mr. Ri were not expected to meet privately. “The secretary has no plans to meet the North Korean foreign minister in Manila, and I don’t expect to see that happen,” Susan A. Thornton, the department’s acting assistant secretary for East Asia and Pacific affairs, said in a briefing on Wednesday.