Friday's launch was only tracked for a short distance and is presumed to have been unsuccessful, the Japan Broadcasting Corp. said.
The broadcaster added that the missile's vertical launch might indicate a newly-developed type of short-range ballistic weapon, quoting Japanese Defense Agency officials.
Sunday's launch, believed to be of a modified land-to-ship missile, has been downplayed by the United States, Japan and South Korea as not being related to Pyongyang's nuclear weapons drive.
"We're not surprised by this. The North Koreans have tested their missiles before. They've had some failures," White House Chief of Staff Andrew Card told CNN television.
Japan, which neighbours North Korea and like the US is also involved in the six-nation process of trying to disarm the self-avowed nuclear power, said it was treating Sunday's test as a "domestic" drill.
"It was like a normal domestic military drill. It has no impact" on Japan's security, said Chief Cabinet Secretary Hiroyuki Hosoda, the government spokesman.