The North has carried out five nuclear tests - two of them a year ago - and expert satellite imagery analysis suggests it could well be preparing for a sixth.
The state media on Saturday reported North Korea has said the USA missile strikes on Syria were an "intolerable act of aggression" and it "proves a million times over" that strengthening its nuclear programme was the right choice.
North Korea considers Syria an ally.
The friendly tone was a far cry from Trump's acerbic campaign denouncements about China's "rape" of the USA economy and his vow to punish Beijing with punitive tariffs.
The move of the Vinson strike group is in response to recent North Korean provocations, the official said.
The talks between Kim and Wu came shortly after Trump hosted Chinese leader Xi Jinping for a summit at which he pressed Beijing to do more to curb the North's nuclear ambitions.
Although China's state media went strong on photos and coverage of the Xi-Trump summit, it gave little space to news of the strikes against Syria, with few editorials or commentaries.
Pentagon sources on Saturday told CNN that US Pacific Command chief Admiral Harry B. Harris Jr. has ordered the Nimitz-class supercarrier and all its support ships towards the Korean peninsula.
The pair discussed a range of issues, including North Korea, which the United States believes is trying to develop an intercontinental ballistic missile capable of hitting the west coast of the US.
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Satellite imagery analysis suggests it could be preparing for a sixth, with USA intelligence officials warning that Pyongyang could be less than two years away from its goal of striking the continental United States.
South Korea and the U.S. have been conducting joint military drills recently, which have been viewed by the North as an act of war and preparation for invasion.
The Chinese commentaries, however, made no mention of the USA missile strike on a Syrian government air base, which overshadowed the summit.
US National Security Adviser H.R. McMaster on Sunday criticised North Korea as a rogue nation engaged in provocative behaviour and said denuclearisation of the peninsula "must happen".
"It's a signal that Trump's administration will not only talk, they will act", said Wang Dong, Associate Professor and Director of the School of International Studies at Peking University.
South Korea's Unification Minister Hong Yong-pyo said Monday that the repercussions of a potential military response were worrying.
Many believed his strike on Syria last week was meant to be a warning to the country and its leaders.
Analysts had earlier said the strikes contained a clear message for Pyongyang that the United States was not afraid to exercise the military option, and there had been speculation as to how the North would respond.
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