According to South Korea's military, the launch came about two hours after the failure of a similar test. The missile covered 400 km (250 miles), more than halfway towards the southwest coast of Japan's main island of Honshu.
The launches and earlier nuclear tests by North Korea is highlights the defiance of the communist nation towards international warnings and a series of U.N. Security Council resolutions and sanctions, which North Korea rejects as an infringement of its sovereignty.
Japanese Defence Minister Gen Nakatani said the second missile reached an altitude of 1,000 km (620 miles).
"We don't know whether it counts as a success, but North Korea has shown some capability with IRBMs (intermediate range ballistic missiles)," he told reporters in Tokyo. "The threat to Japan is intensifying."
North and South Korea are still at war because their 1950-53 conflict ended in an armistice, not a peace treaty. South Korean President Park Geun-hye denounced the test and said: "The North Korean regime must realize that complete isolation and self-destruction await at the end of reckless provocation."
NATO Secretary General Jens Stoltenberg also decried North Korea's "provocative actions". "I strongly condemn the launch by North Korea of two ballistic missiles," Stoltenberg said in a statement.
"These repeated provocative actions ... undermine international security and dialogue," he said, calling for North Korea to "fully comply with its obligations under international law, not to threaten with or conduct any launches using ballistic missile technology and to refrain from any further provocative actions".