"If there is a second summit, that would be an important opportunity for President Trump to empower the secretary of state and subsequent nuclear negotiators to have that ... gravitas and the confidence of the president to negotiate an agreement with North Korea," Pak said at an event discussing the US-South Korea alliance.

The speculation is that Trump and Kim will meet again on the occasion of the United Nations General Assembly in New York next month. But it's still uncertain whether Kim will travel to the international gathering at all.

Trump has drawn flak from his critics for granting Kim a meeting with a US president, an unprecedented move they say gave Pyongyang the legitimacy it seeks on the world stage.

Trump has countered that such meetings, even with leaders of adversarial nations, are a "good thing."

He tweeted shortly after his summit with Kim that the North Korean threat was now over, apparently referring to their statement that committed the North to work toward "complete denuclearization" of the Korean Peninsula.

Negotiations to implement the deal have appeared to stall as the two sides wrangle over the sequencing of confidence-building measures required from each side.

Mike Green, senior vice president for Asia at the Center for Strategic and International Studies, told the same event that the threat is in fact "becoming more serious" because of the North's survivable road-mobile intercontinental ballistic missile capability.

That calls for a "much more robust deterrence posture and much more ability to demonstrate consequences for North Korea," he said, emphasizing the importance of maintaining the US-South Korea alliance. (Yonhap)