Trump said North Korea had "disrespected" China by attempting to launch another ballistic missile as the President counts on his Chinese counterpart Xi Jinping to encourage Pyongyang to give up its pursuit of missile and nuclear weapons programmes.
North Korea's latest missile test came hours after U.S. Secretary of State Rex Tillerson mounted an effort at the United Nations on Friday to rally pressure against Kim Jong Un's regime.
Experts say North Korea has readied a nuclear test, which many suspected would take place earlier in April on the anniversary of the country's founder's birth or the foundation of its military.
South Korea and the USA say the sole objective of THAAD is to guard against North Korean missiles.
Mr Trump refused comment on whether the United States had anything to do with the missile test failure.
Asked if "not happy" with another Pyongyang nuclear test meant he would undertake "military action" against the regime of North Korean leader Kim Jong Un, Trump said, "I don't know".
In CBS' Face The Nation, Trump did, however, say that he would not be "very happy" if Pyongyang moved ahead with another nuclear test. "And I think it's not exactly the right time to call China a currency manipulator right now".
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And later, when congressional GOP members threatened to cut all federal funding to Planned Parenthood, Ivanka approached Richards to "start a broader dialogue".
Elsewhere, Mr Trump's National Security Adviser Lt Gen HR McMaster said Mr Trump "has made clear that he is going to resolve this issue one way or the other", but that the president's preference was to work with China and others to resolve it without military action.
"We have a situation that we just can not let - we can not let what's been going on for a long period of years continue", Mr Trump said.
"The timing of the launch suggested it was calculated to send a message, as North Korea remained under the scrutiny of world powers", said Kim Dong-yub, an expert at Kyungnam University's Institute of Far Eastern Studies in Seoul.
Trump downplayed the significance of North Korea's "small missile launch", which occurred early in the day. This was not a big missile. The North's previous test almost two weeks ago was also botched. "They have tremendous power, and we'll see what happens".
During his presidential campaign, Trump often lashed out at China, calling them a currency manipulator and accusing them of not doing almost enough to stop North Korea's pursuit of nuclear weapons. "We can not protect countries all over the world, where they're not paying us what we need". "So obviously, he's a pretty smart cookie".
"Now that the U.S.is kicking up the overall racket for sanctions and pressure against the DPRK, pursuant to its new DPRK policy called "maximum pressure and engagement", the DPRK will speed up at the maximum pace the measure for bolstering its nuclear deterrence", a spokesman for North Korea's foreign ministry said in a statement carried by its official KCNA news agency. The Vinson is taking part in joint drills with the South Korean Navy, an intentional show of force in response to recent North Korean provocations.
Asked if that means military action, Mr Trump responded: "I don't know. We'll see what happens".