The two reaffirmed their commitment at a joint press conference held after a summit meeting in Tokyo, Xinhua news agency reported.
Abe, for his part, announced that Japan will expand its unilateral sanctions on the DPRK.
Trump's visit to Japan was his first trip to Asia since his inauguration in January and marks the first leg of his five-nation tour of Asia.
The US president will leave Japan on Tuesday for South Korea, before traveling to China and then to Vietnam and the Philippines.