Military options have been prepared and will presented to Trump should Kim's detonate a nuke.
"While I greatly appreciate the efforts of President Xi & China to help with North Korea, it has not worked out".
Trump has praised Chinese President Xi Jinping for trying to contain North Korea, which counts on China for 90 per cent of its trade, but the effort has delivered few results.
North Korea has detained two Korean-American academics and a missionary, a Canadian pastor and three South Korean nationals who were doing missionary work there.
But like his predecessors, Mr. Trump is gradually learning that for all its talk about cooperation, China is deeply reluctant to take any measures that could seriously destabilize the North Korean government, for fear the country might collapse or be absorbed by the South. "He's signaling to others that he understands this isn't working, and he's trying to defend himself, or justify himself, by saying that at least they tried as opposed to others who didn't even try".
China's Foreign Ministry said earlier Beijing had made "unremitting efforts" to resolve tensions on the Korean peninsula for its own interests, not due to external pressure.
"China's efforts to resolve the peninsula nuclear issue is not due to any external pressure, but because China is a member of the region and a responsible member of the global community, and because resolving the peninsula nuclear issue is in China's interests", ministry spokesman Geng Shuang told a daily news briefing.
The Trump administration is considering banning travel by US citizens to North Korea, officials said Tuesday, and Trump declared Warmbier's treatment a "total disgrace".
-North Korean tensions aggravated by dozens of North Korean missile launches and two nuclear bomb tests since past year in defiance of U.N. Security Council resolutions.
American concern is growing over North Korea's acceleration toward having a nuclear missile that can strike the USA mainland.
Top diplomats and defence chiefs from the United States and China began a day of talks in Washington on Wednesday looking for ways to press North Korea to give up its nuclear and missile programs. "For example, we both agree that our companies should not do business with any United Nations -designated North Korean entities", said Tillerson - adding more positive spin on the summit later when he said two delegations also had a "frank exchange of views" on the South China Sea, but that China said it was committed to resolving the disputes there peacefully.
Moon, who is scheduled to visit Washington next week, also said in an interview with CBS on Tuesday he hoped to draw North Korea into negotiations on its nuclear program by the end of the year.
Yun is a US special envoy.
A USA diplomat who traveled to North Korea to secure the release of American college student Otto Warmbier (WORM'-bir) plans to attend his funeral in OH on Thursday.
In a White House meeting with visiting Ukraine President Petro Poroshenko, Trump criticized the way Warmbier's case was handled in the year since his arrest, appearing to assail both North Korea and his predecessor, President Barack Obama. "His family is incredible ... but he should have been brought home a long time ago", Trump said.
Mattis and Secretary of State Rex Tillerson are hosting their Chinese counterparts on Wednesday for the US-China Diplomatic and Security Dialogue in Washington.
The Chinese have moved a bit toward restraining North Korea, but not enough for administration officials' taste - and there is reason to be skeptical as to how much more they will move. -Chinese talks in Washington.
So what did Trump mean by his tweet on Tuesday then?
He said Seoul will exert pressure on Pyongyang but if the regime makes some progress on denuclearization, the issue of reopening the inter-Korean Gaeseong Industrial Complex could be put on the table.