Council diplomats say the U.S. and China, the North's closest ally, have been working on a new sanctions resolution.
The missile flew 787 km (489 miles) on a trajectory reaching an altitude of 2,111.5 km (1,312 miles), KCNA said.
A functional ICBM would need a nuclear warhead that can be mounted on to a missile. The country's official Korean Central News Agency said the test firing of the new ground-to-ground strategic ballistic missile "Hwasong-12" was successful.
The Self-Defense Forces now do not have the ability to hit enemy bases with Tomahawk cruise missiles, for example.
More significantly, the new missile could be a stepping stone to a properly working ICBM - which would fundamentally change assessments of the threat posed by Pyongyang.
Defense Minister Tomomi Inada told a May 15 session of the Upper House Audit Committee that she would listen carefully to such views held in the LDP.
In a statement released on Monday, the 15 members of the UN Security Council strongly condemned Pyongyang's ballistic missile test that occurred over the weekend.
This image made from video of an undated still image broadcast in a news bulletin by North Korea's KRT on Monday shows leader Kim Jong Un at what was said to be a missile test site at an undisclosed location in North Korea.
The U.N. council also plans to convene an emergency session Tuesday to discuss the North Korea issue at the request of the US and Japan.
The members of the Security Council stressed that the DPRK's "illegal ballistic missile activities are contributing to its development of nuclear weapons delivery systems and are greatly increasing tension in the region and beyond", the statement said.
Russian Federation borders the peninsula along the north-eastern edge of North Korea. Pundits believe Pyongyang's latest provocation will provide a hard litmus test for South Korea's newly-elected President Moon Jae-in.
The North is banned from testing missiles using ballistic technology under multiple UNSC resolutions that have been adopted since 2006.
North Korea is known to be developing both nuclear weapons - it has conducted five nuclear tests - and the missiles capable of delivering those weapons to their target.
State media paraphrased North Korea's leader as saying that "the most flawless weapon systems in the world will never become the eternal exclusive property of the US", warning that "the USA should not ... disregard or misjudge the reality that its mainland and Pacific operation region are in (North Korea's) sighting range for strike".
"More important", he added, it "might represent a substantial advance to developing an intercontinental ballistic missile".
Spicer said Donald Trump looks forward to having a conversation with the new South Korean President and discussing the way forward. "If the U.S. dares opt for a military provocation against [us] we are ready to counter it".
Russian President Vladimir Putin said the test was risky, but warned against attempts to "intimidate" Pyongyang. The aircraft carrier USS Carl Vinson, which was ordered to the region last month, is still in the Sea of Japan, where the missile landed Sunday.
The UN Security Council was weighing its response to the latest launch, with diplomats saying that the United States was pushing for a toughly-worded statement of condemnation.