South Korea's military has said the Scud-type missile travelled eastward for 450 km (280 miles).
"We will never tolerate North Korea's continued provocations that ignore repeated warnings by the global community", said Japan PM Shinzo Abe.
Last week, Marine Lt. Gen. Vincent Stewart, director of the Defense Intelligence Agency, said if North Korea's growing nuclear threat is not monitored and stopped, Kim would eventually succeed in fielding a nuclear-armed missile that could possibly reach the U.S.
Turkey on Monday evening strongly condemned a ballistic missile launch by North Korea earlier in the day.
Riki Ellison, the founder of the Missile Defense Advocacy Alliance based near Washington which advocates for the development and deployment of missile defense systems to defend the United States, described the test as "vital".
The short-range missile flew for six minutes before landing in the Sea of Japan, the US Pacific Command said, adding it was working on a more detailed assessment.
Concerns about North Korean nuclear and missile threats have deepened in the USA since North Korean leader Kim Jong-un said in his New Year's Day address that the country is ready to test-fire an intercontinental ballistic missile apparently capable of reaching the U.S.
While it appears to be a test of whether the United States military can counter a North Korean launch, the Pentagon said the exercise is testing the US' capability to knock down any threatening missiles, including from Iran, CNN reported.
Rodong Sinmun, the official newspaper of the Central Committee of the Workers' Party of Korea, earlier reported that South Korea has developed a new high-precision guidance system, allowing ballistic missiles to hit targets within an accuracy of seven meters.
While the U.S. administration works to solidify a policy to deal with North Korea's nuclear ambitions, the new liberal president of South Korea has signalled he will be flexible in expanding civilian exchange with the North.
The U.S. military on Tuesday successfully intercepted an intercontinental-range missile for the first time, a key test of its missile-defense system amid heightening tensions with North Korea.
And if a diplomatic solution isn't possible, what would a war with North Korea look like?
South Korea said it looks like North Korea plans to go ahead with its nuclear weapons and missiles programs, no matter what the rest of the world thinks. He has signaled an interest in expanding civilian exchanges with North Korea, but it's unclear if he'll be able to push anytime soon for major rapprochement while the North continues to make serious advances in its nuclear and missile programs. "We insist on a political resolution through peaceful means".