Council President Francois Delattre of France said the Security Council would likely meet later in the day on the back-to-back tests of new medium range missile.
"We favor a quick and firm reaction of the Security Council," he said.
"The North Korean ballistic program is a serious threat to regional and international peace and security," he said. "Confronted by the threat of proliferation we consider that weakness is not an option."
The first test was deemed to have failed after the missile flew an estimated 150 kilometers (90 miles) over the East Sea, or Sea of Japan.
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Japanese military monitors said the second test attained a height of 1,000 kilometers and a range of 400 kilometers.
Four previous Musudan tests this year failed either on their mobile launch pad or shortly after take-off.
Several UN Security Council resolutions ban North Korea from engaging in nuclear or ballistic missile activity.
After Pyongyang conducted a fourth nuclear test on January 6, followed by a long-range rocket launch February 7, the Security Council adopted its most punishing sanctions yet against North Korea.