A senior Chinese envoy is reportedly scheduled to visit South Korea to discuss the controversial deployment of a USA missile system in the South, to which Beijing is opposed, as well as North Korea's nuclear and missile programs.
Mr Trump said he believes he made "tremendous progress" in the US-China relationship during talks with Mr Xi.
"The president has asked them to be prepared to give us a full range of options to remove that threat", he said on Fox News, apparently referring to Trump's advisers.
Trump looked to be in good humour, while Xi wore a rare, sustained smile while posing for photos at the Mar-a-Lago resort in Florida, noted observers. "And I think that's a very, very important symbolization of the growing rapport between the two countries", Ross said.
Tillerson said Trump and the Chinese president "had extensive discussions around the unsafe situation in North Korea".
In Tokyo, the feasibility of USA military action was downplayed, while South Korea said the focus remained on deterrence and readiness.
South Korean and US forces are also involved in annual joint military drills that run until the end of April.
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They include placing more missile defenses in the region, having a greater US military presence on the seas, and sanctioning anyone, including Chinese firms and individuals, that does business or facilitates business with the Kim regime. It is unsurprising, in that context, that North Korea would see giving in to U.S. calls for unilateral disarmament as merely a prelude to a USA attack.
However, whether the USA would, in fact, take military action against North Korea is a different story, given the covert nature of Pyongyang's nuclear and missile programs and its growing weapons capabilities that could cause "tremendous damage in the region", added Blinken, who also served as deputy national security adviser to former President Barack Obama.
Wu Dawei's visit - set to last up to five days - comes at a time of heightened inter-Korean tensions, with expectations running high that North Korea could soon conduct a sixth nuclear test.
-China summit meeting on Thursday and Friday, in which North Korean issues were discussed.
The South Carolina Republican also wants additional penalties imposed on Russia for what he calls Moscow's "aiding and abetting" of Syrian President Bashar Assad (bah-SHAR' AH'-sahd) in the use of chemical weapons - and for Russian meddling in the 2016 American election.
Zhang Tuosheng, an expert from the China Foundation for worldwide and Strategic Studies, said: "Neither the U.S. nor North Korea would take the initiative to wage a war, but the risk of conflict is higher as a small miscalculation or accident could bring war to the peninsula".
An expert who has authored a book on North Korea said Saturday not to be surprised if North Korean leader Kim John Un went into hiding following the USA missile strike against Syria, stating in an email to Fox News that American military power was more than likely something he had "dismissed before".