Mr Ri was avoided by Mr Tillerson, who skipped a group dinner attended by his North Korean counterpart.
Washington is leaving it to China to restate world powers' opposition to new nuclear bomb tests while the United States urges a halt in missile launches "which obviously is a much lower rhetorical barrier to resuming talks", the official said.
Ri did not respond publicly.
It called the latest test of the Hwasong-14 intercontinental ballistic missile "a stern warning" to the U.S., saying it is time America learns to "coexist with us". Last month, it test-launched two intercontinental ballistic missiles capable of reaching the USA mainland.
The US-drafted resolution imposed a full ban on North Korea's exports of coal, iron, iron ore, lead, and lead ore, as well as fish and seafood. The US believes the United Nations sanctions will not work unless China stops Chinese firms that continue to do business with the North. Tens of thousands of them return hard currency to the increasingly isolated regime.
"We actually had very thorough talks", Wang said afterwards.More news: Shares hit by US-North Korea tensions
North Korea said the sanctions infringed its sovereignty and it was ready to give Washington a "severe lesson" with its strategic nuclear force in response to any USA military action.
"We want to make sure China is continuing to implement fully the sanctions regime", she said. Very big financial impact!
Foreign Minister Ri Yong Ho also says that his country has no intention of using nuclear weapons against any country "except the U.S".
At the same time, China urged the USA not to increase tensions, saying it had reached a critical point.
In a front page commentary on Monday, the overseas edition of the ruling Communist Party's official People's Daily said North Korea had to be punished for flouting United Nations rules with its missile launches but sanctions also had to be targeted to avoid hurting ordinary people or other countries.
President Donald Trump praised the Security Council's action and US resolve.More news: Political tensions continue to weigh on world stocks
"It's not that easy but it is a direction we need to work together towards", Wang said of the six-country talks, which used to be hosted by China and were stopped in 2009. The resolution is expected to cut the country's $3 billion annual export revenue by a third. The Trump administration is cautiously embracing China's apparent newfound cooperation.
China's government - North Korea's neighbor, chief political ally and economic lifeline - has supported the sanctions in word. "At the end of the day, it will take more than sanctions".
"Sanction is necessary, but sanction is not the ultimate objective", Wang told reporters.
Leonid Petrov, a North Korea expert at the Australian National University, said China had given the appearance it had delivered on its promise to Trump. "They never have and likely never will". North Korea has tested missiles, including an ICBM, seven times since April.
"China is the essential player", Lefkowitz said.
U.S. State Secretary Rex Tillerson, left, poses with Philippine President Rodrigo Duterte during the former's courtesy call at Malacanang Palace in Manila, Philippines, Monday, Aug. 7, 2017.More news: Zillow Group, Inc. (NASDAQ:Z) Rating Reiterated by Cowen and Company
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