But the surprise US military response to Syrian President Bashar Assad's apparent chemical weapons attack on civilians threw a wild card into the summit.
McMaster said, when asked why the Navy strike group Carl Vinson, whose flagship is a nuclear-powered aircraft carrier of that name, will make its way toward the Korean peninsula from Singapore as a show of force.
Tillerson said President Trump's trip to China would be a "state visit" in 2017, but gave no other details.
Secretary of state Rex Tillerson said the two nations "agreed to increase cooperation and work with the global community to convince North Korea to peacefully resolve the issue and abandon its weapons programmes".
President Xi arrived at Trump's Mar-a-Lago Florida resort on Thursday.
The Syrian opposition has reported that Assad's forces have begun flying again from an air base struck last week by US missiles, and Graham says Assad is telling Trump - "F. you' - by resuming those flights". "And so I think this is a wrongheaded notion, that we just skip the most important step - and that is whether or not we should go to war".
"There is a difference between Syria and North Korea", Yamamoto said.
In Tokyo, the feasibility of USA military action was downplayed, while South Korea said the focus remained on deterrence and readiness.
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Before the meeting at his Mar-a-Largo estate, Trump was reportedly presented with options to respond to the North's nuclear weapons program including placing US nukes in South Korea or assassinating North Korean leader Kim Jong Un.
Donald Trump seemed to have broken the ice with China with the help of his grandchildren.
Trump had joked to reporters on Thursday that he had "gotten nothing, absolutely nothing" from his first meeting with Xi - but they had developed a friendship he was sure would become "a very, very great relationship".
Washington denies it has any intention of invading the North.
The response by North Korea's foreign ministry, carried by the official KCNA news agency, was the first since U.S. warships in the Mediterranean Sea launched dozens of missiles at a Syrian air base which the Pentagon says was involved in a chemical weapons attack earlier in the week.
To rein in Pyongyang's nuclear and ballistic missiles programs, Japan and the United States agree that the role of China, the main economic and diplomatic benefactor of North Korea, is crucial.
The North has carried out five nuclear tests - two of them past year - and expert satellite imagery analysis suggests it could well be preparing for a sixth. Not long after dinner the USA announced the missile barrage on an air base in Syria in retaliation for a chemical weapons attack against civilians.
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.