Details of the launch, including the type of missile, were scant, but Mr Trump backed early criticism by Japanese prime minister Shinzo Abe, who is on a visit to the US.
As the leaders held a brief press conference in Palm Beach, Florida, Mr Abe called North Korea’s reported launch “absolutely intolerable”.
There was no immediate confirmation from the North, which had recently warned it is ready to test its first intercontinental ballistic missile.
The reports come days before the North is to mark the birthday of leader Kim Jong Un’s late father, Kim Jong Il.
At the president’s south Florida estate, Mr Trump followed Mr Abe’s condemnation with even fewer words, saying in part: “I just want everybody to understand and fully know that the United States of America stands behind Japan, its great ally, 100%.”
Mr Abe read a brief statement in which he called on the North to comply fully with relevant United Nations Security Council resolutions.
He said Mr Trump had assured him of US support and that the president’s presence showed his determination and commitment.
South Korea’s joint chiefs of staff said the missile was fired early on Sunday from around Banghyon, in North Pyongan province, which is where South Korean officials have said the North test-launched its powerful mid-range Musudan missile on October 15 and 20.
The military in Seoul said that the missile flew about 310 miles, but news agency Yonhap said that while determinations were still being made, it was not believed to be an intercontinental ballistic missile (ICBM).
The missile is believed to have splashed down into the sea between the Korean Peninsula and Japan.
Japan’s chief cabinet cecretary Yoshihide Suga said the missile did not hit Japanese territorial seas.
The North conducted two nuclear tests and a host of rocket launches last year in continued efforts to expand its nuclear weapons and missile programmes.
Kim Jong Un said in his New Year’s address that the country has reached the final stages of readiness to test an ICBM, which would be a major step forward in its efforts to build a credible nuclear threat to the United States.
Though Pyongyang has been relatively quiet about the transfer of power to the Trump administration, its state media has repeatedly called for Washington to abandon its “hostile policy” and vowed to continue its nuclear and missile development programmes until the US changes its diplomatic approach.
Just days ago, it also reaffirmed its plan to conduct more space launches, which it staunchly defends, but which have been criticised because they involve dual use technology that can be transferred to improve missiles.
Kim Dong-yeop, an analyst at the Institute for Far Eastern Studies in Seoul, speculated the missile could be a Musudan or a similar rocket designed to test engines for an intercontinental ballistic missile that could hit the US mainland.
Analysts are divided, however, over how close the North is to having a reliable long-range rocket that could be coupled with a nuclear warhead capable to striking US targets.
South Korea’s acting president and prime minister Hwang Kyo-ahn said his country would punish North Korea for the missile launch.
According to the Foreign Ministry, South Korea will continue to work with allies including the United States, Japan and the European Union to ensure a thorough implementation of sanctions against the North and make the country realise that it will “never be able to survive” without discarding all of its nuclear and missile programmes.