President Park Geun-hye and U.S. President Barack Obama agreed Thursday to closely cooperate to ensure that the U.N. Security Council can adopt a resolution for strong sanctions on North Korea over its hydrogen bomb test, Cheong Wa Dae said.

The two leaders also shared the view that the international community must make sure that North Korea pays the corresponding price for a nuclear test, the South Korean presidential office said.

The 20-minute telephone conversation came a day after North Korea claimed it had succeeded in conducting a hydrogen bomb test.

The North's test prompted the U.N. Security Council to hold an emergency session on Wednesday and to agree to immediately start work on a new sanctions resolution against North Korea. The council "strongly condemns" Pyongyang's latest nuclear test.

North Korea has already been under U.N. sanctions for its three previous nuclear tests in 2006, 2009 and 2013.

Obama also vowed to take all necessary measures for the security of South Korea. Park expressed thanks to Obama for reaffirming the U.S. commitment to the security of South Korea, according to Cheong Wa Dae.

In Washington, the White House said Obama reaffirmed the "unshakeable U.S. commitment" to South Korea's security, and the two leaders agreed to work together to forge a united and strong international response to North Korea's latest reckless behavior.

"The two leaders condemned the test and agreed that North Korea's actions constitute yet another violation of its obligations and commitments under international law, including several U.N.

Security Council Resolutions," the White House said in a statement.

Park and Obama also shared the need of coordinating a stance with China in dealing with North Korea's hydrogen bomb test.

Chinese support is crucial in adopting a new resolution for sanctions as it is one of the veto-wielding five permanent members of the council. The four other members are the U.S., Britain, France and Russia.

China is a traditional ally of North Korea and is believed to have significant leverage over North Korea, but Pyongyang's latest nuclear test showed that Beijing's influence is limited.

The bilateral ties -- once described as being as close as "lips and teeth" -- have been strained over the North's defiant pursuit of nuclear ambition.

Also Thursday, South Korea plans to hold a new session of the National Security Council at the presidential office, Defense Minister Han Min-koo said. (Yonhap)