The North Korean leader, Kim Jong-un, has said missile tests have given his country "the sure capability to attack US interests in the Pacific".
He called Wednesday's twin tests a "great event" that strengthened the country's nuclear attack capacity.
The US and South Korea say the first test failed but the second showed what Japan called "some capability".
UN resolutions ban the North, which is developing nuclear weapons, from using ballistic missile technology.
The Musudan missile has an estimated range of 3,000km (1,800 miles), far enough to hit the US territory of Guam.