Earlier this month, Mr. Trump said China isn't a currency manipulator after meeting with Chinese President Xi Jinping about North Korea.
"We do have to do something" with partners in the region and globally "that involves enforcement of the United Nations sanctions that are in place", McMaster said on "Fox News Sunday". "It may mean ratcheting up those sanctions even further".
When asked to clarify, the U.S. president said: "I would not be happy".
North Korea test-fired a missile over the weekend in apparent defiance of a concerted United States push for tougher global sanctions to curb Pyongyang's nuclear weapons ambitions. But he understands we're not going to be very happy. "And if that happens, we can't allow it to happen".
China is the North's main trading partner and the USA president has been urging Beijing to try to rein in the reclusive state's military activities.
Pressed by Dickerson on whether he means there could be military action, Trump did not confirm, but he also did not deny.
Trump, who admitted North Korea was his biggest global challenge, said the launch was an affront to the North's sole main ally - China.
"The U.S. National Security Adviser H.R. McMaster explained that the recent statements by President Trump were made within the context in line with the general U.S. public expectations on burden-sharing with allies", a South Korean presidential office spokesperson told NBC News. "We'll see what happens", the president said.
Pence Promotes Trump's Economic Plans, Visits USS Rondald Reagan in Japan
President Trump met with Chinese President Xi Jinping in a summit early April to negotiate cooperation between the two countries. On Tuesday, while visiting Tokyo , he called the North Korea regime "the most ominous threat" to the region.
In the CBS interview, the president was asked why the North's rockets keep blowing up.
Tensions have been rising on the Korean Peninsula amid missile tests by the reclusive and unpredictable communist regime in North Korea, which possesses nuclear weapons and is working on a intercontinental ballistic missile capable of reaching the U.S.
"I'd rather not discuss it", he said.
Trump also called North Korea's leader "a pretty smart cookie" for being able to hold onto power after taking over at a young age.
"Just in the past two weeks, the world witnessed the strength and resolve of our new president in actions taken in Syria and Afghanistan", he said. "They certainly don't want to see nuclear on - from their neighbor", he said of China.
On Sunday, Mr Trump spoke to the leaders of Thailand and Singapore to discuss the North Korean threat while extending an invitation for both to visit Washington, the White House said. "That, as we would say, trumps trade".
Priebus said the president is looking for cooperation in the region to work "with as many partners in the area as we can get".
Such routine condemnation and a series of sanctions resolutions since 2006, when North Korea conducted its first nuclear test, have done little to impede its push for ballistic missiles and nuclear arms.