North Korea launched two missiles within hours of each other, with one flying about 400km (250 miles) and reaching an altitude of 1,000km.
A confirmed successful test would mark a step forward for North Korea after four failed launches in recent months.
South Korea, the US and Nato have also expressed alarm over the latest tests.
Both launches are believed to have been intermediate-range Musudan missiles, whose range of about 3,000km is enough to hit South Korea, Japan and the US territory of Guam in the Western Pacific
A suspected first launch failed, South Korean officials said, travelling about 150km before landing in the sea.
But the second showed what Japanese Defence Minister Gen Nakatani called "some capability".
"I believe the missiles are a serious threat to our country," he said.
North Korea, which is developing nuclear weapons, is banned by UN resolutions from any use of ballistic missile technology.
In January it conducted its fourth nuclear test, claiming it as its first use of a hydrogen bomb. Shortly after that it launched a satellite, widely seen as a test of long-range missile technology.