The call came after Pyongyang had earlier launched at least four missiles, with three splashing down in the sea close to key US ally Japan.
The launches present a challenge for US President Donald Trump, who has described North Korea as a "big, big problem" and vowed to deal with the issue "very strongly."
South Korea said four missiles were fired from Tongchang County in North Pyongan province into the East Sea — its name for the Sea of Japan.
The missiles traveled about 1,000 kilometers (620 miles) and reached an altitude of 260 kilometers (160 miles), a spokesman for South Korea's Joint Chiefs of Staff said.
Monday's launches were the latest in a series of test-firings that violate UN resolutions barring Pyongyang from developing missile technology.
White House spokesman Sean Spicer said North Korea poses a "very serious threat," adding the Trump administration was taking steps to "enhance our ability to defend against North Korea's ballistic missiles."
Such defenses include the planned deployment to South Korea of a missile-defense system called THAAD.
US Defense Department spokesman Navy Captain Jeff Davis suggested North Korea had attempted to launch more than four missiles and these were medium-range rockets, not ICBMs.
"There were four that landed. There may be a higher number of launches, but we are not commenting on" that, the Pentagon spokesman said.
Seoul and Washington last week began annual joint military exercises that always infuriate Pyongyang, drawing the North's military warning of "merciless nuclear counter-action."
Under leader Kim Jong-Un, Pyongyang wants to develop an intercontinental ballistic missile (ICBM) capable of reaching the US mainland — something Trump has vowed would not happen.
Japanese Prime Minister Shinzo Abe said three of the North Korean missiles came down in Tokyo's Exclusive Economic Zone (EEZ) — waters extending 200 nautical miles from its coast.
"This clearly shows North Korea has entered a new stage of threat," Abe told parliament.
The emergency UN meeting is likely to be scheduled on Wednesday when ambassadors return from a visit to the Lake Chad region in Africa, diplomats said.
America's ambassador to the UN, Nikki Haley, said on Twitter that the world "won't allow" North Korea to continue on its "destructive path."