North Korea called its sixth and most powerful nuclear test a “perfect success” but its neighbours and other world leaders criticised the hydrogen bomb blast.
Mr Trump said on Twitter that the North’s “words and actions continue to be very hostile and dangerous” to the US.
He called it “a rogue nation which has become a great threat and embarrassment to China, which is trying to help but with little success”.
China is by far the North’s biggest trading partner, but Mr Trump appeared to be more critical of South Korean President Moon Jae-in, who has attempted to reach out to the North.
“South Korea is finding, as I have told them, that their talk of appeasement with North Korea will not work, they only understand one thing!” Mr Trump tweeted.
Though the precise strength of the blast has yet to be determined, the artificial earthquake it caused was several times stronger than tremors generated by its previous tests. It reportedly shook buildings in China and in Russia.
The test was carried out at 12.29pm local time at the Punggye-ri site where North Korea has conducted nearly all of its past nuclear tests. Officials in Seoul put the magnitude at 5.7 while the US Geological Survey said it was a magnitude 6.3.
North Korea’s state-run television broadcast a special bulletin on Sunday afternoon to announce the test.
It said leader Kim Jong Un attended a meeting of the ruling party’s presidium and signed the go-ahead order.
Earlier in the day, the party’s newspaper ran a front-page story showing photos of Kim examining what it said was a nuclear warhead being fitted on to the nose of an intercontinental ballistic missile.
North Korea in July test-launched two ICBMs that are believed to be capable of reaching the mainland United States. That would be a major step forward for Pyongyang, which says its missile development is part of a defensive effort to build a viable nuclear deterrent that can target US cities.
China’s foreign ministry said that the Chinese government has “expressed firm opposition and strong condemnation”. It urged North Korea to “stop taking erroneous actions that deteriorate the situation”.
South Korea held a National Security Council meeting chaired by President Moon Jae-in. National Security Director Chung Eui-yong said Mr Moon will seek every available measure, including new UN sanctions or the deployment of more US military assets, to further isolate Pyongyang.
Japan’s Prime Minister Shinzo Abe called the test “absolutely unacceptable”.
The nuclear test is the North’s first since US President Donald Trump assumed office in January. Mr Trump has been talking tough with the North over its stepped-up missile tests, including a comment that Pyongyang would see fire, fury and power unlike any the world had ever witnessed if it continued even verbal threats.
North Korea conducted two nuclear tests last year, the last nearly a year ago, on the September 9 anniversary of the nation’s founding.
It has since maintained a fast pace in weapons tests, including its first two intercontinental ballistic missiles test in July. Last month, North Korea fired a potentially nuclear-capable mid-range missile over northern Japan.
Earlier on Sunday, photos released by the North Korean government showed Kim talking with his lieutenants as he observed a device that was apparently the thermonuclear weapon destined for an ICBM.
Another photo showed a diagram on the wall behind Kim of a bomb mounted inside a cone.
State media said Kim visited the Nuclear Weapons Institute and inspected a “homemade” H-bomb with “super explosive power” that “is adjustable from tens (of) kiloton to hundreds (of) kiloton”.
North Korea’s nuclear and missile programme has made huge strides since Kim rose to power following his father’s death in late 2011. The North followed its two tests of Hwasong-14 ICBMs by threatening in August to launch a salvo of its Hwasong-12 intermediate range missiles toward the US Pacific island territory of Guam.
It flew a Hwasong-12 over northern Japan last week, the first such overflight by a missile capable of carrying nukes, in a launch Kim described as a “meaningful prelude” to containing Guam, the home of major US military facilities, and more ballistic missile tests targeting the Pacific.
French President Emmanuel Macron condemned “in the strongest possible terms” North Korea’s sixth nuclear test.
Mr Macron said he “calls on the members of the United Nations Security Council to quickly react to this new violation by North Korea of international law”.
He said the international community “must treat this new provocation with the utmost firmness” to bring North Korea back to the path of dialogue and give up its nuclear and missile programmes.
The Russian Foreign Ministry said North Korea’s claim to have tested a hydrogen bomb “deserves the strongest condemnation”.
A spokesman called for immediate dialogue and negotiations, saying that is the only way to settle the Korean Peninsula’s problems, “including the nuclear one”.
The ministry said Russia reaffirms its readiness to participate in negotiations, “including in the context of the implementation of the Russian-Chinese road map”.
Under that proposal, North Korea would suspend nuclear and missile tests in exchange for the US and South Korea suspending their joint military exercises.