"North Korea's repeated provocative action went against our government and global community's expectations and desire to establish peace and denuclearisation on the Korean peninsula", said Foreign Ministry spokesman, Cho June-Hyuck.
South Korean Unification Ministry spokesman Lee Duk-haeng told reporters the government's most basic stance is that communication lines between South and North Korea should reopen.
At the request of diplomats from the U.S., Japan and South Korea, a United Nations' Security Council consultation on the missile test will take place Tuesday.
There is skepticism about North Korea's claims about its re-entry technology, which is needed to return a warhead to the atmosphere from space so it can hit its intended target.
The state-run KCNA news agency said the weapon was now ready to be deployed for military action.
The U.S. can no longer wait for the repressive North Korean state to collapse under the weight of worldwide sanctions, Litwak argued, but instead must make a realistic deal that would allow Pyongyang to maintain its current nuclear and ballistic missile arsenal in exchange for suspending further tests and development.
Japanese news agencies said the missile probably fell into the sea outside Japanese waters.
The launch was also seen as a test of the new South Korean administration of Moon Jae-in who took office earlier on May 10.More news: Jones hoping to play against Ajax in Europa League final
Missile tests such as Sunday's present a hard challenge to Moon, a liberal who took over as South Korea's president on May 10 and has expressed a desire to reach out to the North. Pyongyang's aggressive push to improve its weapons program also makes it one of the most urgent foreign policy concerns for the Trump administration.
The North conducted two nuclear tests previous year.
They emphasised "the vital importance" of the DPRK immediately "showing honest commitment to denuclearization" through concrete action and stressed the importance of working to reduce tensions in the Korean Peninsula and beyond, it said. With a nuclear warhead it could deal a considerable blow to the deployment of US reinforcement troops to the Korean Peninsula. Many more weapons capable of striking the United States will be launched from this land. Liquid-fuel missiles, on the other hand, are generally fueled at the launch site in a process that can last an hour and requires fueling and other vehicles.
They also agreed to "react to the latest provocation in a resolute manner" through steps including those at the United Nations Security Council, it said.
On Monday, North Korea's regime issued a statement claiming that its new rocket could deliver a "large heavy nuclear warhead" all the way to the USA mainland.
The high altitude and long flight time - 30 minutes, the US said - indicate a missile with an extended range, according to David Wright, co-director of the Union of Concerned Scientists. North Korea's media said more missiles will be launched in the future.
Later on Sunday, Secretary of State Rex Tillerson told Fox News that North Korea nuclear testing was "disappointing, disturbing".