South Korean President Moon Jae-in held a National Security Council meeting at the presidential Blue House to discuss the missile launch, Moon's office said.
The U.S. government is increasing vigilance on North Korea's improvements in missile technology.
The North has vowed to develop a missile mounted with a nuclear warhead that can strike the mainland USA, saying the programme is necessary to counter US aggression.
Lee said communications were severed by North Korea past year, in the wake of new sanctions following North's last nuclear test and Pyongyang's decision to shut down a joint industrial zone operated inside the North.
North Korea fired a ballistic missile on Sunday that landed in the sea near Russian Federation, which experts said signaled major advances in developing an intercontinental ballistic missile that could target the United States.
U.S. Ambassador to the United Nations Nikki Haley speaks while Japan's U.N. Ambassador Koro Bessho (L) looks on during a press encounter ahead of an emergency meeting of the U.N. Security Council at the United Nations in NY, U.S., May 16, 2017. What would you think would happen if North Korea used a nuclear weapon against the United States?
North Korea has repeated test launches to obtain the technology needed for reentry into the atmosphere, which is said to be technically very hard.
Polish left-wingers urge support for Labour in United Kingdom election
Corbyn should be given a fair chance at leading the country, while 56% said he would be a "disaster" as prime minister. He said: "If circumstances arose where that was a real option, it would represent complete and cataclysmic failure".
There is still uncertainty as to whether the United States might ask South Korea to pay for THAAD, the U.S. missile shield deployed against North Korean missiles.
North Korea is not a threat to the United States.
A date and other specifics of the summit are still to be decided, Yoon said. However, Moon is now seeking a two-track policy of sanctions and dialogue.
"The state of the alliance is strong and I am fully confident that it will only grow stronger between our two administrations", Pottinger said.
South Korea's new President Moon has admitted that a war with North Korea is by far not unlikely.
A TV screen shows images of U.S. President Donald Trump, left, and North Korean leader Kim Jong Un during a news program at the Seoul Railway Station in Seoul. However, Washington remains Seoul's closest ally and military protector. The country was without a president, as Moon's predecessor Park Geun-hye had been impeached and jailed and acting president Hwang Kyo-ahn had no real mandate.
The South Korean military has said that the descending rate of the Hwasong-12 missile was somewhere between Mach 15 and 24, which falls short of the minimum falling rate of Mach 24 that any intercontinental ballistic missile would have recorded.