Tillerson met Chinese Foreign Minister Wang after chairing a high-level session at the UN Security Council on North Korea here yesterday.
The meeting came just hours before North Korea test-fired another ballistic missile but it "failed" to go beyond its territory.
The Chinese state-run Xinhua news agency said in a report that two sides agreed the current situation on the Korean Peninsula poses a challenge.
Tillerson, chairing the UNSC meeting as President of the Council, had asserted that Washington's goal is "not regime change" in the isolated country nor does it "desire to threaten the North Korean people or destabilise the Asia Pacific region."
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He, however, warned that no options are off the table in dealing with the nuclear threat posed by North Korea.
Tillerson told the Chinese Foreign Minister that the two sides have launched cooperation in a constructive way on international and regional issues including the nuclear issue of the Korean Peninsula, by which the United States is encouraged.
Wang said the historical meeting between Chinese PresidentXi Jinpingand US President Donald Trump at the Mar-a-Lago estate in Florida was a complete success, with relations between Washingon and Beijing achieving a smooth transition with a good start.
This was a positive sign that the two sides are willing to cooperate for the well-being of the two peoples and to jointly contribute to world peace, Wang said.
Wang noted that close communication between leaders of the two countries plays an important and leading role in the development of bilateral ties.
Noting that China and the United Stateshave established four high-level dialogue mechanisms, Wang said that the two sides should move forward to reach more consensuses and manage differences well so as to ensure the healthy and stable development of bilateral ties.
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