Mr Trump assured Japan's Prime Minister Shinzo Abe that "America stands behind Japan, its great ally, 100%".
The missile fired by North Korea flew east towards the Sea of Japan for about 500km, South Korean officials say.
Mr Abe said the test was "absolutely intolerable". Japanese officials say the missile did not reach its waters.
Speaking at a joint press conference during a visit to the US, Mr Abe added that Mr Trump had also assured him that he was committed to "further enforcing our alliance".
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Image copyrightAP Image captionDonald Trump said that the US "stands behind Japan 100%"[/caption]North Korea has conducted a number of nuclear tests in the past year in acts of aggression that continue to alarm and anger the region.
Sunday's launch took place at 07:55 local time (22:55 GMT Saturday) from the Banghyon air base in North Pyongan province on the west side of the Korean peninsula.
The missile reached an altitude of about 550km (350 miles), according to a South Korean official quoted by Reuters news agency, and appeared to be a Rodong medium-range missile.
South Korea's foreign ministry said that "North Korea's repeated provocations show the Kim Jong-un regime's nature of irrationality, maniacally obsessed in its nuclear and missile development".
Japan's Chief Cabinet Secretary Yoshihide Suga confirmed the missile had not reached Japanese territorial waters, adding that Tokyo would make a "strong protest" to North Korea over the incident.
There has so far been no comment from North Korea.
North Korean leader Kim Jong-un said in January that the country was close to testing long-range missiles capable of carrying nuclear warheads.
On a visit to South Korea last week, US Defence Secretary James Mattis said that any use of nuclear weapons by North Korea would be met with an "effective and overwhelming" response.
He also reconfirmed plans to deploy a US missile defence system in South Korea later this year.
North Korea conducted its fifth test of a nuclear device last year, and claims it is capable of carrying out a nuclear attack on the US, though experts are still unconvinced that its technology has progressed that far.
It has also said in recent weeks that it has a new intercontinental ballistic missile, capable of reaching the US mainland, which it is prepared to test launch at any time.
