The President was briefed about the launch while the missile was in the air.
"It is a situation that we will handle," Mr Trump told reporters.
Mr Trump was in a meeting with Senate Republicans on Capitol Hill to discuss the upcoming tax reform bill.
This is the first test the hermit kingdom has conducted in two months, its 20th overall, and its seventh actual launch of a weapon. On 15 September North Korean leader Kim Jong-un launched an intermediate ballistic missile over the coast of Hokkaido island in northern Japan which landed in the Pacific Ocean.
South Korea's military says the missile was fired from an area north of Pyongyang early on Wednesday morning local time.
The Pentagon tracked the trajectory of the weapon and spokesman Colonel Rob Manning said the missile was launched from Sain Ni, North Korea, and travelled about 620 miles (1,000 km) before landing in the Sea of Japan.
It also reportedly went approximately 2,800 miles (4,000 km) up into the atmosphere, according to South Korean and Japanese authorities. US Defence Secretary James Mattis said the latest missile did fly higher than previous ones.
He warned that North Korea continues to strengthen its nuclear weapons programme with weapons that "threaten everywhere in the world."
Japan's chief Cabinet secretary Yoshihide Suga has said the missile may have landed in his country's exclusive economic zone, or the area of the sea which Japan has control over. No damage has been reported as yet.
The country's United Nations Ambassador Koro Bessho said it has sent a message to North Korea "that we criticize their behaviour in the strongest terms possible."
South Korea's presidential office said it was holding a National Security Council meeting early Wednesday morning local time to discuss possible action.
Seoul's Joint Chiefs of Staff said it had conducted a "precision strike" drill but did not offer any more detail.
The US State Department has officially condemned the missile launch and urged countries to continue strict economic sanctions against Pyongyang. Secretary of State Rex Tillerson announced the US and Canada will convene a meeting of UN member countries to discuss next steps.
The launch comes just one week after the US declared North Korea a state sponsor of terrorism.
The move was mostly related to economic sanctions but also meant as a message to North Korea and its supporters.
Mr Tillerson called the designation as "very symbolic...practical effects may be limited but hopefully clos[es] off loopholes" in existing sanctions for "dual use" product exports that can be used by civilian and military end-users within North Korea.
Those products require separate licenses to sell under US export regulations.
North Korea was last on the state-sponsored terror list in 2008, under the George W Bush administration. It was removed that year in a bid to salvage a deal halting its nuclear development.
Mr Tillerson said that attempt at negotiations "obviously failed."
He noted that North Korea's fuel supply "is already quite constrained" as shown by "anecdotal evidence" and US intelligence sources which show cars lined up at petrol stations or certain stations closing that would normally have fuel.
The issue there is that the country only has one refinery that operates internally so they are heavily reliant on finished fuel imports.
The latest missile launch also adds to mounting tensions between Mr Trump and Mr Kim.
The pair have publicly traded insults throughout the year. The US President gave Mr Kim the nickname "Rocket Man" and referred to him as such during the president's speech in front of the United Nations General Assembly.
Mr Kim’s state news agency then issued a statement in which they referred to Mr Trump as a “dotard."
Mr Trump had recently tweeted that Secretary of State Rex Tillerson was "wasting his time" trying to negotiate with Mr Kim through State Department diplomatic backchannels.
He tweeted that "only one thing will work" to deter North Korea's development of its nuclear arsenal, in yet another indication the president thinks military action is the only option left.
In September, a US intelligence official said they had no reason to doubt Mr Kim and his military had developed a hydrogen bomb and in July, officials said they believed North Korea had been able to make a nuclear warhead capable of fitting on an intercontinental ballistic missile – claiming missiles will have the range to reach the US.
South Korea and Japan have been preparing for a possible nuclear attack by running drills for residents, including the approximately 67,000 Americans stationed on military bases in both countries.
Hawaii is also preparing an air siren warning system and informing the public to shelter in place and have food and medical supplies on hand at all times.
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