The two leaders strongly condemned North Korea's latest nuclear provocation as a serious and escalating threat.

"The two leaders shared a view on the need for the strongest pressure and sanctions against North Korea to deter North Korea's provocative activities and make it start taking steps toward denuclearization," he said.

Earlier reports suggested the leaders were set to announce an agreement for Seoul's acquisition or development of nuclear-powered submarines, a strategic asset that could counter North Korea's submarine-launched ballistic missiles. Seoul earlier dismissed the reports.

The Cheong Wa Dae spokesman refused to confirm whether Seoul's acquisition of the most advanced military assets would include nuclear-propelled submarines.

Their second bilateral summit was watched closely as it came two days after Trump warned of a possible military action against Pyongyang.

In his first address to the UN General Assembly, also attended by North Korea, the US leader said his country will have no choice but to "totally destroy North Korea" if forced to defend itself or its allies.

Trump's remarks followed the North's sixth and apparently most powerful nuclear test so far, staged Sept. 3.

Moon expressed satisfaction with what he called the United States' "firm" reaction to the North's latest nuclear provocation.

"North Korea's latest provocation is very deplorable, and it greatly outraged us, but the US firmly and greatly responded and I am very satisfied that cooperation between South Korea-US was realized without any gap," he said while meeting with Trump, according to Cheong Wa Dae pool reports.

"President Trump has also delivered a very powerful speech at the UN General Assembly and I am confident such power will certainly change North Korea," he added.

Immediately following their bilateral summit, Moon and Trump were joined by Japanese Prime Minister Shinzo Abe for a three-way summit over lunch.

The three leaders vowed to put maximum pressure on North Korea.

"The three leaders noted North Korea's nuclear and missile development posed a grave threat to peace in Northeast Asia and the world and that they cannot accept this," South Korean Foreign Minister Kang Kyung-wha told a press briefing.

"Under such understanding, the leaders of the three countries agreed on the need for the international community to put maximum pressure and sanctions to the level that North Korea cannot withstand and voluntarily come to the dialogue table," she added.

The Japanese leader also called for additional measures.

"Recently, UN sanctions were adopted unanimously. These are very powerful measures. But we need more," Abe said, according to Cheong Wa Dae pool reports.

Trump introduced his new executive order, enhancing the Treasury Department's authority to target any individuals or entities that conduct "significant trade in goods, services or technology with North Korea."

Moon welcomed the new step.

"I believe the United States' unilateral step, through the executive order President Trump just mentioned...will have a great impact on our strive to achieve North Korea's complete denuclearization. I again thank President Trump who has made a firm decision, and promise that South Korea too will do its utmost to support the measure," he said. (Yonhap)