Admitting that the U.S. is considering re-listing North Korea as a state sponsor of terrorism Mr McMaster said: "The President's Cabinet is looking at this as part of the overall strategy on North Korea".
Under legislation enacted August 2, the State Department was required to determine within 90 days - or around Thursday - whether North Korea meets the criteria for being designated as a state sponsor of terrorism.
McMaster said Trump, who has approved a variety of sanctions against North Korea while pressing China to do more, is at the beginning of his drive for Pyongyang to give up nuclear weapons. It will be the second stop of his 12-day trip to five countries.
In a swifter visit, Mr Trump will visit American and South Korean service members, and again call on the global community to place further pressure onNorth Korea.
Trump is on his way to the South Korean capital, Seoul, during his first trip to Asia.
The report said the U.S.is quietly pursuing direct diplomacy with North Korea, quoting an unnamed senior State Department official.
Ahead of Trump's visit to Asia, the drills involving the nuclear-capable USA bombers marked the latest show of force by the United States and its allies.
Separately, two US officials said a decision may be made for the three aircraft carriers now in the Asia Pacific region to carry out an exercise to coincide with Trump's trip. McMaster also hinted that Trump is unlikely to tone down his rhetoric on North Korea during his upcoming Asia trip, insisting the regime's behavior was to blame instead for recent tensions.
"And then.a lot of leaders across the world, and the president foremost among them, discrediting this ideology jihadist ideology", he said and praised the Saudi crown prince's speech during which he called for a return to moderate Islam.
"The U.S. imperialist warmongers should not act rashly".
Herbert Robert McMaster who advises the White House on terrorism said that Kim Jong-un's regime appeared to fit the list's criteria following the murder of the leader's half-brother earlier this year.
"The president will use whatever language he wants to use", he said.
"You sense the anxiety, you sense the fear, you sense that this is something different that the Koreans are facing".
His goal will be to increase worldwide support for an effort to deprive North Korea of resources as leverage to coerce it to give up nuclear weapons.
South Korea's Moon is ruling this out.
Re-designating North Korea as a state sponsor of terrorism would be largely of symbolic significance.
Trump will address the National Assembly before flying from South Korea to Beijing. There he will ask Chinese President Xi Jinping to do more to rein in North Korea.
China is North Korea's only remaining significant ally.
"China is definitely doing more but obviously it is not enough until all of us achieve denuclearisation", General McMaster said.