Such remarks by US top diplomatic and security officials come amid predictions of another major provocation by North Korea this month, including a possible sixth nuclear test that some analysts say could be up to 14 times more powerful than the last.
On the issue of North Korea, Abe and Trump also "completely agreed" on the importance of solidarity among Japan, the United States and South Korea, according to the prime minister.
"If you violate global agreements, if you fail to live up to commitments, if you become a threat to others, at some point a response is likely to be undertaken", Tillerson told ABC's "This Week".
He says he thinks Xi "wants to help us with North Korea", Trump said of Xi, crediting China with taking a "big step" by turning back boats of coal that North Korea sells to its northern neighbor. Meanwhile, in response to the increased tensions in the region, the US has responded by sending an aircraft carrier group close to the Korean peninsula.
McMaster described the US decision to send the Carl Vinson Strike Group to safeguard USA interests in the Western Pacific as "prudent".
North Korea has pledged to bolster its defenses to protect against such airstrikes.More news: Bruins clinch playoff berth with 4-0 win over Lightning
But in what could be seen as a possible change on China's North Korea policy, Beijing's foreign ministry released a rather refrained quote to Washington's uncommon decision to send back its USS Carl Vinson strike group near the Korean peninsula, in contrast to widely expected strong opposition comments. The North called the USA action in Syria "absolutely unpardonable" and said it proves that its nuclear weapons are justified to protect the country against Washington's "evermore reckless moves for a war". The report did not name the official, which is common in KCNA reports.
Pyongyang continues to be a thorn in the side of the USA and its regional allies, and North Korea remains unrepentant, refusing to modify its nuclear weapons program or come to the negotiating table. Asked on ABC if development of an intercontinental missile was a "red line" for Trump, Tillerson said: "If we judge that they have perfected that type of delivery system, then that becomes a very serious stage of their further development".
On Sunday's political talk shows, top officials in President Trump's administration gave different assessments of Trump's goals in Syria and involving Russian Federation, following his Thursday strike on one of Syrian President Bashar al-Assad's air bases.
China has agreed to "strong" new measures to punish North Korea if it carries out a nuclear test, Seoul said on Monday after the U.S. signalled it may act to shut down Pyongyang's weapons programme.
In their 20-minute conversation, Trump said he emphasized the importance of the Seoul-Washington alliance and spent a lot of time during the summit discussing the Korean Peninsula.
He didn't specify North Korea, but the context was clear enough.