It was Tillerson's first meeting with the 10-member Association of Southeast Asian Nations (ASEAN), and he is expected to seek their support for taking the necessary steps to end North Korea's nuclear weapons program.
The top USA diplomat said Washington is preparing additional sanctions if North Korea's actions warrant them.
Diplomats say USA pressure has caused some irritation in ASEAN, including Malaysia, which has maintained relations with Pyongyang in spite of the assassination of North Korean leader Kim Jong-un's estranged half brother at Kuala Lumpur International airport in February.
The region's top diplomats will likely be more focused on the Trump administration's trade policy and its dealings with China and what it means for US policy toward the South China Sea, where several members of the bloc have territorial disputes with Beijing. Eight of them host North Korean embassies and five have embassies in Pyongyang.
U.S. Secretary of State Rex Tillerson (C) shakes hands with ASEAN foreign ministers before a working lunch at the State Department in Washington, U.S., May 4, 2017.
Washington said there was a shared concern among the Southeast Asian bloc that North Korea's provocation has threatened the stability and peace in the Asia-Pacific region and around the globe.
"And so countries have agreed, and in some cases have limited the size or reduced the size of the North Korean diplomatic presence in their countries", Murphy said.
A 2002 Declaration on the Conduct of Parties in the South China Sea is legally non-binding.
According to Murphy, Tillerson called on ASEAN countries to fully implement U.N. sanctions on Pyongyang, which is working to develop a nuclear-tipped missile capable of reaching the United States, and to show a united front on the issue.
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Southeast Asian nations generally welcome cordial ties between the two powers but worry about whether secret deal-making might undercut Washington's willingness to stand up to China, which claims virtually all the South China Sea and has conflicting territorial claims with four ASEAN nations. He emphasized the importance of economic and trade ties between the US and Southeast Asia.
"We think that more can be done, not just in Southeast Asia", he said.
On the issue of the South China Sea, Asean has recently adopted a cautious approach.
The top US diplomat planned to visit the Philippines in August to attend several ASEAN regional meetings.
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"In some circumstances, if you condition our national security efforts on someone adopting our values, we probably can't achieve our national security goals or our national security interests", Tillerson said.
This year marks the 40th anniversary of the establishment of the ASEAN-US dialogue relations. "This is a big market, our fourth largest trading partner", he said.
During his speech, Tillerson added that not always asking foreign countries to adopt USA values "doesn't mean that we leave those values on the sidelines". US officials are also asking China to urge more China-friendly ASEAN members, such as Laos and Cambodia, to do the same.
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