South Korean President Moon Jae-in and US President Donald Trump agreed to remove the limit on the payload of South Korean missiles under the allies' missile guideline in a move to enhance South Korea's own defense capabilities against North Korean provocations, Seoul's presidential office Cheong Wa Dae said Tuesday.

The agreement was reached in a telephone conversation between the two leaders held late Monday.

"President Moon held a telephone conversation with US President Donald Trump between 10:45 p.m. and 11:25 p.m. (Seoul time) and discussed countermeasures against North Korea's sixth nuclear test in-depth," Cheong Wa Dae spokesman Park Soo-hyun said in a press release.

As an "effective" countermeasure, the two agreed to remove the limit on the payload of South Korean missiles under the Korea-US missile guideline, he added.

The agreement followed weeks of discussions between defense and foreign officials of the two countries to increase the weight of South Korean missile payloads as a way of beefing up deterrence against North Korean provocations.

North Korea staged its sixth nuclear test Sunday.

"President Moon noted the condition was very concerning in that the latest nuclear test showed more power than any previous tests and that North Korea itself has claimed the test involved a hydrogen bomb to be mounted on intercontinental ballistic missiles," Park said.

The US president agreed on the need for what his South Korean counterpart earlier called the most powerful and practical measures against the North that the communist state can feel keenly, according to the Cheong Wa Dae spokesman.

Trump also promised to work closely together with South Korea, he added.

The call between Moon and Trump also came after what many here viewed as a possible rift between the two allies over how to rein in the communist state's evolving nuclear and missile technologies.

Since taking office in May, the new South Korean president has consistently urged the reclusive North to return to the dialogue table.

Trump, on the other hand, has repeatedly warned the North of dire consequences, once saying the communist state will be met by "fire and fury" if it continues to make threats against the US and its allies.

In a Twitter message posted shortly after Pyongyang's latest nuclear provocation on Sunday, the US president also insisted South Korea was "finding, as I have told them, that their talk of appeasement with North Korea will not work."

In their latest conversation, the US and South Korean leaders apparently failed to stress the need for dialogue with the reclusive North.

"The two leaders shared a view that at this moment, they need to put the strongest pressure and sanctions on North Korea, and agreed to push for a stronger U.N. Security Council sanctions resolution as part of such efforts," the Cheong Wa Dae spokesman said.

Later, the White House said the two leaders noted the "grave threat" the North's latest provocation posed to the entire world.

"The two leaders agreed to maximize pressure on North Korea using all means at their disposal," it said in a brief statement on the outcome of their talks.

"They also pledged to strengthen joint military capabilities," it added, noting the US president gave his "in-principle" approval to lift the restriction on South Korea's missile payload capabilities.

The two agreed to hold further discussions at various levels of their governments and to hold talks at the upcoming U.N. general assembly to be held in New York later in the month. (Yonhap)