"I am very disappointed in China," Trump wrote in a pair of Twitter posts. "...they do NOTHING for us with North Korea, just talk. We will no longer allow this to continue. China could easily solve this problem!"
Friday's test was designed to show the Hwasong-14 missile's maximum range with a "large-sized heavy nuclear warhead," a statement from Pyongyang's Korean Central News Agency said.
"The whole US mainland" is now within North Korea's reach, KCNA quoted Kim as saying. The North Korean leader called Pyongyang's weapons program "a precious asset" that cannot be reversed or replaced, according to the agency.
On Sunday, North Korea said it will "respond with firm action" if the US continues to pursue sanctions against it, according to KCNA, quoting a foreign ministry spokesman.
"The US needs to stop with its delusion of trying to harm us, by clearly understanding the strategic status of the DPRK which soared up as the world's nuclear and missile power, and our military and peoples' strong will to revenge our enemies to destruction," the spokesman said.
"If the US continues to frantically cling on to the so-called 'strong sanctions' and military adventures against us, we will respond with firm action of justice that we had already made clear," the spokesman added.
Expert: Missile test puts US mainland in range
Weapons experts say if Friday's missile had been fired on a flatter, standard trajectory, it would have threatened major US cities. Los Angeles, Denver and Chicago would all be well within its range, with the possible ability to reach as far as New York and Boston, according to David Wright, a missile expert at the Union of Concerned Scientists.
However, early analysis of Friday's test cannot determine how heavy a payload the missile was carrying in its warhead, Wright said. The heavier the payload, the shorter the range.
But if North Korea's assertions about Friday's test are true, Pyongyang may be even more advanced in its missile program than previously thought.
Earlier in the week, a US official told CNN the United States believed that North Korea would be able to launch a reliable nuclear-capable intercontinental ballistic missile by early 2018.
The official said that while North Korea can currently get a missile "off the ground," a lot of undetermined variables remain about guidance, re-entry and the ability to hit a specific target.
China to North Korea: Stop escalating tensions
China, a longtime North Korean ally, issued a statement Saturday condemning the missile launch and asked Pyongyang to "stop taking actions that would escalate tensions" on the Korean Peninsula.
"The UN Security Council has clear regulations on North Korea's launch activities that use ballistic missile technologies. China is opposed to North Korea's launch activities in violation of UN Security Council resolutions and against the will of the international community," Chinese Foreign Ministry spokesman Geng Shuang said.
Beijing's statement reiterated its long-held position on North Korea's missile program.
But Trump said in his tweets Saturday night that China has been taking advantage of the US. He tied trade policy to the North Korea situation and took a swipe at his predecessors in the Oval Office.
"Our foolish past leaders have allowed them (China) to make hundreds of billions of dollars a year in trade" while allowing North Korea's missile program to become a direct threat to the US mainland, he wrote.
China earlier this year proposed that North Korea freeze its nuclear weapons and missile programs in exchange for the United States and South Korea ending a string of military exercises that North Korea considers a threat to its security.
B-1 bombers fly over Korean Peninsula
The Trump administration has answered Pyongyang's missile tests with displays of US military power, including missile tests of its own.
On Sunday, the US Missile Defense Agency announced that it had conducted a "successful" test of its Terminal High Altitude Area Defense THAAD system in Alaska, intercepting a medium-range ballistic missile fired from a US military aircraft over the Pacific Ocean. It was the 15th such test.
Continuing another trend, the US on Saturday sent two B-1 bombers from Andersen Air Force Base in Guam on a 10-hour round trip over the Korean Peninsula in what the US Pacific Air Forces called a direct response to the North Korean missile test.
The B-1s teamed up with Japanese and South Korean fighter jets to test "combined capabilities" during the mission, the US military said in a statement.
"Diplomacy remains the lead; however, we have a responsibility to our allies and our nation to showcase our unwavering commitment while planning for the worst-case scenario. If called upon, we are ready to respond with rapid, lethal, and overwhelming force at a time and place of our choosing," Gen. Terrence J. O'Shaughnessy, Pacific Air Forces commander, said in the statement.
While Washington continues its military pressure, it has also asked China to pressure North Korea economically to cut off its access to foreign currency.
Beijing says it has slashed imports of coal from North Korea, but trade between the two countries is rising.
A Chinese government official said in mid-July
that China-North Korea trade was worth $2.6 billion in the first half of 2017, up about 10% over the same period last year.
Trump criticized Beijing over the North Korean trade situation via Twitter in early July.
"So much for China working with us - but we had to give it a try!" he tweeted.
Zhang Baohui, a professor of political science at Hong Kong's Lingnan University, said Saturday's tweets from Trump show his policy on North Korea has been a failure.
"Trump has cornered himself on the North Korea issue -- now how can he climb down? North Korea defies him, the only action he can take now is with US-China relations," Zhang said.