His Japanese counterpart, Shinzo Abe, who has adopted a more forceful approach toward North Korea than his predecessors, appeared open to the suggestion, saying his country would take all steps necessary to protect itself from threats emanating out of Pyongyang.
The back-and-forth during a news conference here reflected the change in tone both the United States and Japan have taken as threats from North Korean dictator Kim Jong Un have scaled up in recent months.
Trump, responding to reports he wanted Japan to shoot down a North Korean missile that passed over its territory, said Monday the country should be protecting itself.
"He will shoot them out of the sky when he completes the purchase of a lot of military equipment from the United States," Trump said of Abe, with whom he sat for talks earlier in the day.
Abe responded by saying his government already buys a lot of military equipment from the US, but agreed with Trump the country needs "to enhance our defense capability."
"Missile defense is something based on cooperation between Japan and the US," he said, adding "if it is necessary" to shoot down a missile "of course we will do that."
Abe has pressed Japan to revise its pacifist constitution -- ratified following World War II -- that specifically bars the country from maintaining a military. Japan does maintain self-defense forces, and analysts have said any revision to the constitution would be largely cosmetic.
But the move does underscore Abe's commitment to confronting North Korea directly, an approach that breaks with his predecessors who relied more heavily on the United States for protection against outside threats.
Trump has maintained that countries should bear responsibility for their own defense, and has aggressively pursued arms sales agreements in the name of weaning other nations off US-provided security.
In Japan, the threat became more acute in September when North Korea fired a ballistic missile over the northern island of Hokkaido. Reports in Japanese media suggested this week that Trump wanted Japanese forces to down the missile, and Trump appeared to confirm that desire on Monday.
After Trump's previous offers to sell military equipment to Japan and South Korea in the name of counting North Korea, the regime lashed out, calling the President a "war merchant and strangler of peace."