North Korean leader Kim Jong-un has claimed a series of technological breakthroughs in developing missiles.
Japan has warned North Korean missiles pose "a serious threat" after the country carried out new tests in defiance of international sanctions.
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 Defense 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 a hydrogen bomb. Shortly after that it launched a satellite, widely seen as a test of long-range missile technology.
This is at least the fifth test of the Musudan medium-range missile in the past few months and while most have ended in failure, one of the latest pair fired does seem to have travelled at a high trajectory for some 400km.
The Musudan appears to be based on the technology of an old Russian Soviet-era submarine launched missile. It is carried on a wheeled launcher and was first seen in parades back in 2003, though it was never test-fired until April of this year.
Experts believe the weapon is intended to be able to strike US bases on Guam, but North Korea's ultimate goal is to be able to threaten the continental United States.
North Korea's progress is mixed and erratic. But it is clearly determined and its missile and associated nuclear weapons programme means that its rocket tests are being carefully watched by Washington.
South Korea's Joint Chiefs of Staff said Seoul and the US were "carrying out an in-depth analysis" of the second missile, and did not say whether they considered it a success.
Several analysts were less cautious though. Jeffrey Lewis, of the California-based Middlebury Institute of International Studies, tweeted: "That's a successful test folks."
In other reaction:
- South Korean president, Park Geun-hye, condemned North Korea's "reckless provocations"
- The US warned the tests would only increase international efforts to stop North Korea's weapons programme
- Nato Secretary General Jens Stoltenberg said the launches "undermine international security and dialogue"
- China, North Korea's only major ally, said the North "should avoid doing anything to further worsen tensions".
North Korea is thought to have dozens of Musudans but has never conducted a full-distance test.
The four other missiles tested in the past two months either exploded mid-air or crashed.
