South Korea was seeking "the toughest retaliation measures" after the North tested another nuclear weapon, a national security official said.
"President Moon Jae-In ordered the toughest retaliation measures against North Korea's ICBM level missile and nuclear provocations, mobilizing all diplomatic means to totally isolate North Korea," Chung Eui-Yong, director of the national security office in the South Korean president's office, said on Sunday in a nationally televised press briefing.
"President Moon also ordered to find ways to nullify North Korea's nuclear facilities and display our military's capability to retaliate," Chung said. "He will never tolerate North Korea's advancement in its nuclear capabilities and will deploy U.S. assets."
South Korea earlier raised its military alert level, placing all troops on high alert.
Chung added that he had talked with H.R. McMaster, the U.S. national security adviser, both before and after South Korea's National Security Council held a meeting. The two agreed that the U.S. and South Korean presidents would talk on the phone soon to discuss cooperation on measures against North Korean provocation, he said.
North Korea said on state television on Sunday afternoon that it successfully carried out a test of a hydrogen bomb intended to be carried by an intercontinental ballistic missile.
A hydrogen bomb is much more powerful than the simpler types of atomic weapons tested by North Korea five times previously, or the bombs dropped on Japan during World War II. H-bombs are also harder to develop.
North Korea's announcement followed reports of as many as two tremors in the rogue state at around noon local time, which officials in South Korea and Japan had said appeared to be the country's sixth nuclear test.
South Korea already has deployed the U.S.-supplied Terminal High Altitude Area Defense (THAAD) system, which could bring down a missile coming out of North Korea.
The defense shield s designed to intercept and destroy ballistic missiles in mid-air.
But it's been a point of contention with China, which has called for its removal, and with the North.
China's foreign ministry on Sunday also urged North Korea to stop its "wrong" actions, adding it urged the isolated nation to respect the U.N. Security Council resolutions, Reuters reported.
Beijing earlier agreed to ban imports of North Korean iron, lead, and coal as part of new U.N. sanctions. Trade between the two countries is also down.
The mainland's foreign ministry said on Sunday it would comprehensively implement the resolutions, with a firm stance on denuclearization of the Korean peninsula, Dow Jones reported.
Japan said that McMaster told his Japanese counterpart on Sunday that the U.S. is committed to defending the country, including using a nuclear deterrent, Reuters reported.
Japanese Prime Minister Shinzo Abe said his country would take all possible measures to ensure the safety and security of his people. He added that Japan would collaborate with other countries on the impact of radioactive materials from the nuclear test.
In the aftermath of two July intercontinental ballistic missile tests, the United Nations last month hit North Korea with "the most stringent set of sanctions placed on any country in a generation," according to U.S. Ambassador to the U.N. Nikki Haley.
Previous U.N. penalties have resulted in Pyongyang expressing its displeasure and demonstration of its iron-clad nuclear ambition through more missile tests.
Russia's foreign ministry also said North Korea's actions had created a "serious threat for peace and security" in the region, Reuters reported.
—CNBC's Nyshka Chandran and Stacey Yuen contributed to this article.