Mr Trump issued the warning during a briefing on opioid addiction at his golf course in Bedminster, New Jersey.
A Japanese defence paper and a US media report said that North Korea may have successfully produced a miniaturised nuclear warhead that can fit inside its missiles.
That is a key benchmark in the country’s attempt to become a fully-fledged nuclear power.
The Washington Post story, citing unnamed US intelligence officials, said the confidential analysis was completed last month by the US Defence Intelligence Agency.
Separately, Japan’s defence ministry assessed in a report that it is possible that North Korea has achieved the miniaturisation of nuclear weapons and has developed nuclear warheads.
Washington’s alarm over North Korean leader Kim Jong Un’s pursuit of a nuclear capability has intensified in the past month after the North conducted two tests of intercontinental ballistic missiles last month.