President Trump assured reporters that the Trump White House "will handle" the North Korean crisis, an issue he says he inherited from his predecessors.

"We have a lot of tremendous things going on. We have some interesting situations we'll handle -- North Korea, Middle East, lots of problems we inherited from previous administrations -- we'll take of them, well take of them very well," he said.

When pressed further on how exactly he would "take care" of the North Koreans, he told reporters, "We'll handle North Korea, we'll be able to handle North Korea, it will be handled, we handle everything."

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The North launched a intercontinental ballistic missile (ICBM), its second successful test of this type of long-range missile, late Friday night.

North Korea's first ICBM test was conducted on July 4. Former U.S. ambassador to the United Nations, Bill Richardson, described that test to CBS News as a "game changer" because Kim Jong Un is "basically saying to President Trump 'come at me.'"

As the U.S. assesses its next steps, officials are facing the fact that, in many ways, they are too late. An unstable and unpredictable regime has developed its nuclear missile technology faster than anticipated, and President Trump has limited options, CBS News correspondent Julianna Goldman noted. Analysts say Friday's launch proves that North Korea could be capable of hitting the U.S. mainland, including Los Angeles and possibly Chicago, New York and close to Washington, D.C.

In response, the U.S. conducted a missile defense test Sunday using a Terminal High Altitude Area Defense (THAAD) anti-missile system in Alaska, the U.S. Missile Defense Agency (MDA) said in a statement.

Sunday's test marked the 15th successful intercept out of 15 THAAD tests, and it was carried out to collect "threat data" from an interceptor, the MDA said.

The president expressed his frustration over the recent developments, tweeting on Saturday night that he was "disappointed" in China, and that country does "NOTHING for us" when it comes to North Korea. He complained about the trade imbalance between the U.S. and China, which is the largest trade deficit the U.S. has with any country with which it trades.

"I am very disappointed in China. Our foolish past leaders have allowed them to make hundreds of billions of dollars a year in trade, yet... they do NOTHING for us with North Korea, just talk," Mr. Trump tweeted.

The tweets marked the latest case of Mr. Trump urging Chinese President Xi Jinping to do more regarding North Korea.

When asked about his relationship with Xi at a press conference with French President Emannuel Macron earlier this month, Mr. Trump called Xi "a friend," but added, "We asked him for some assistance with respect to North Korea. Probably he could do a little bit more but we'll find out."

China has countered that it shouldn't be held responsible for solving the nuclear standoff with North Korea, and that it doesn't hold the key to resolving the issue.

On Sunday, the Chinese Mission to the U.N. said in a statement to CBS News that China "is concerned about the current developments."

It added that North Korea should "abide by the relevant resolutions of the [United Nations] Security Council and stop taking action that could lead to further escalation of the situation on the peninsula."

CBS News' Pam Falk contributed to this report.