WASHINGTON (Reuters) -The U.S. commitment to deterrence against North Korea is backed by the full range of U.S. capabilities, including nuclear, U.S. President Joe Biden told South Korean President Yoon Suk Yeol in a meeting on Thursday on the sidelines of a NATO summit.

The two leaders also authorised a guideline on establishing an integrated system of extended deterrence for the Korean peninsula to counter nuclear and military threats from North Korea, Yoon's office said.

The guideline formalises the deployment of U.S. nuclear assets on and around the Korean peninsula to deter and respond to potential nuclear attacks by the North, Yoon's deputy national security adviser Kim Tae-hyo told a briefing in Washington.

"It means U.S. nuclear weapons are specifically being assigned to missions on the Korean Peninsula," Kim said.

Earlier Biden and Yoon issued a joint statement announcing the signing of the Guidelines for Nuclear Deterrence and Nuclear Operations on the Korean Peninsula.

"The Presidents reaffirmed their commitments in the U.S.-ROK Washington Declaration and highlighted that any nuclear attack by the DPRK against the ROK will be met with a swift, overwhelming and decisive response," it said.

DPRK is short for North Korea's official name, the Democratic People's Republic of Korea. ROK refers to South Korea's formal name, the Republic of Korea.

Cheong Seong-Chang, a security strategy expert at the Sejong Institute and a strong advocate of South Korea's own nuclear armament, said the new nuclear guideline is a significant progress that fundamentally changes the way the allies will respond to a nuclear threat from North Korea.

"The problem is, the only thing that will give South Korea full confidence is a promise from the U.S. of an immediate nuclear retaliation in the event of nuclear use by the North, but that is simply impossible," Cheong said.

"That is the inherent limitation of nuclear deterrence," he said, adding whether the nuclear guideline will survive a change in U.S. administration is also questionable.

Yoon's office said the guideline itself is classified.

North Korea has openly advanced its nuclear weapons policy by codifying their use in the event of perceived threat against its territory and enshrining the advancement of nuclear weapons capability in the constitution last year.

Earlier this year, it designated South Korea as its "primary foe" and vowed to annihilate its neighbour for colluding with the United States to wage war against it, in a dramatic reversal of peace overtures they made in 2018.

Both Seoul and Washington deny any aggressive intent against Pyongyang but say they are fully prepared to counter any aggression by the North and have stepped up joint military drills in recent months.

Yoon reaffirmed South Korea's support for Ukraine, pledging to double its contribution to a NATO trust fund from the $12 million it provided in 2024, his office said. The fund enables short-term non-lethal military assistance and long-term capability-building support, NATO says.

It made no mention of any direct military support for Ukraine. Yoon's office has said it was considering weapons supply for Kyiv, reversing its earlier policy of limiting its assistance to humanitarian in nature.

(Reporting by Brendan O'Brien, Ismail Shakil in Washington, Jack Kim in Seoul; Writing by Katharine Jackson and Jack Kim; Editing by Sandra Maler and Michael Perry)