Asked if "not happy" signified "military action", Trump answered: "I don't know".
He added: "And if that happens, we can't allow it to happen".
North Korea test-launched a missile on Saturday that appeared to have failed within minutes, its fourth successive failed launch since March.
"So, their sixth nuclear test is what it would be, combined with the ballistic missile program that poses a grave threat to the United States and our citizens, as well as our friends and partners in the region", he said.
The US is deploying a naval strike group led by an aircraft carrier to the Korean peninsula, and a missile- defense system called Terminal High Altitude Area Defence (THAAD) will be operational "within days", according to officials.
Residents in the village of Seongj, where the missile defense system is being installed, scuffled with police on Sunday.
McMaster says Trump "has made clear that he is going to resolve this issue one way or the other, and what we prefer to do is to work with others, China included, to resolve this situation short of military action".
Analysts say the KN-17 is a new Scud-type missile developed by North Korea.
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South Korea's foreign ministry denounced the launch as an "obvious" violation of United Nations resolutions and the latest display of North Korea's "belligerence and recklessness".
In the interview with Face the Nation, the President was asked why North Korea's rockets keep blowing up.
The president went on to criticize previous Republican and Democratic administrations for their handling of North Korea's nuclear ambitions.
"I don't know", he said.
But both China and Russian Federation rebuked Washington's threat of military force at a meeting of the U.N. Security Council on the matter. It was likely a medium-range KN-17 ballistic missile and broke up minutes after launch, the Associated Press reported, citing an unidentified US official.
Some analysts say a missile the North test fired April 5, which USA officials identified as a Scud variant, also might have been a KN-17.
South Korean media reports said the CIA chief arrived in South Korea over the weekend for meetings with the head of South Korea's National Intelligence Service and high-level officials in the presidential office.
The North is technically still at war with the South after their 1950-53 conflict ended in a truce, not a treaty, and regularly threatens to destroy the United States, Japan and South Korea.
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