Vice President Mike Pence is seeking to reassure and refocus American allies on the growing nuclear threat from North Korea with visits to Japan and South Korea this week.
China will send a special envoy to North Korea, state media said Wednesday, after US President Donald Trump concluded an Asian tour to rally support against Pyongyang's nuclear threats.
The resolution sponsored by the European Union and Japan was adopted without a vote by the General Assembly's human rights committee.
The trip presents a crucial international test for a president looking to reassure Asian allies worried that his inward-looking "America First" agenda could cede power in the region to China.
Tillerson said Washington would be willing to talk to the North if its leaders accept that they must disarm.
Republican senator Graham said that Trump has told him he would go to war to destroy North Korea rather than allow it to develop a long-range nuclear-armed missile.
While on talks with South Korea President Moon Jae-In, Trump made clear that he was in no mood to pursue diplomacy with a regime he accused of having no respect for human life.