Foreign Minister Wang Yi told his North Korean counterpart Ri Yong Ho that Pyongyang's provocations are "reaching the tipping point" when the two met in Manila on August 6 on the sideline of the Association of Southeast Asian Nations Regional Forum.
Cambodia is a key regional ally of China, which this week said it would pay the biggest price from new United Nations sanctions against North Korea because of its close economic ties with the country.
Speaking about the economic sanctions announced by the UN Security Council, Tillerson said: "We hope again that this ultimately will result in North Korea coming to the conclusion to choose a different pathway, and when the conditions are right then we can sit and have a dialogue around the future of North Korea so that they feel secure and prosper economically".
North Korea also said it will take a unspecified action and will never allow its nuclear program to be negotiated on.
The standoff is expected to dominate Monday's Asean Regional Forum, which gathers 27 foreign ministers, including former participants in the halted six-party talks - Russia, Japan, the United States, China and North and South Korea.
Stop testing missiles for an "extended period", Tillerson said, and the USA might deem North Korea ready to talk.
He also said, however, that it could be a turning point for negotiations over North Korea's nuclear proliferation, which led the U.N. Security Council to impose more sanctions on North Korea and its exports on Saturday.
"It was a good outcome", Tillerson said of the United Nations vote, before a meeting with South Korean Foreign Minister Kang Kyung-Wha.
Chinese Foreign Minister Wang Yi urged "the North Korean side to calmly handle the resolutions".
In an interview with MSNBC's Hugh Hewitt, Mr McMaster said Mr Trump has been "deeply briefed" on the strategy on North Korea.
Ri re-affirmed Pyongyang's position on the matter during the meeting, Wang said.
Last year, North Korea sought dialogue partnership with Asean but it has been rejected because of the security situation in the Korean Peninsula. All countries are now banned from importing North Korean coal, iron, lead and seafood products, and from letting in more North Korean laborers whose remittances help fund Kim Jong Un's regime. China, which is a permanent member of the UNSC with a veto power, opted to vote for the sanctions.
"Sanction is necessary, but sanction is not the ultimate objective", Wang told reporters.
ASEAN also prides itself on unity despite disputes, and North Korea sent people to this month's ASEAN event, one of Pyongyang's few forays overseas.
But scholars suspect a US role.
Foreign Minister Kang Kyung-wha made the statement at the ASEAN Regional Forum (ARF) in the Philippine capital of Manila on Monday. However, in a characteristically fiery editorial before the latest sanctions were approved, the North's ruling party newspaper Rodong Sinmun warned against the USA aggression.
It will be the first such meeting since U.S. President Donald Trump took office in January.
The resolution also prohibits countries from expanding intakes of North Korean labourers, bans new joint ventures with North Korea and makes any new investment in existing joint ventures off limits.
And North Korea, for its part, should stop launching missiles and conducting nuclear tests.
Separately, Southeast Asian officials were still trying to reach consensus on a customary communiqué that was supposed to have been released on Saturday, reflecting differences about how to address disputes involving Beijing in the South China Sea.