South Korean President Moon Jae-in headed back to Seoul on Wednesday after a hectic visit here highlighted by talks with US President Donald Trump and a speech at a UN session.

Moon had his ninth summit with Trump on Monday, in which they discussed ways to make headway in working-level nuclear talks between Pyongyang and Washington that will resume soon.

They reaffirmed the principle of avoiding hostile acts against Pyongyang and help it move toward a bright future in case of denuclearization.

The agreement has effectively provided a boost to the Korea peace process, which has been going relatively slowly since the no-deal Hanoi summit between Trump and North Korea's leader Kim Jong-un in late February.

Pyongyang also carried out a series of missile and other projectile launches in recent months.

Moon expressed hope for a third Kim-Trump summit, saying it would be a "truly historic moment in world history."

Moon and Trump also demonstrated the robust alliance between their countries.

But Trump presented an "alliance bill," demanding South Korea pay more for the US Forces Korea and apparently pressing Seoul to purchase more US weapon systems.

Addressing the 74th session of the UN General Assembly Tuesday, Moon suggested transforming the Demilitarized Zone, which cuts across the middle of the Korean peninsula, into an international peace zone.

"If the DMZ comes to house UN offices already stationed in the two Koreas and other international organizations related to peace, ecology and culture and emerges as a center for research on peace, peacekeeping, arms control and trust building, it can become an international peace zone in name as well as substance," he said.

Delivering a separate speech at the UN Climate Action, he unveiled Seoul's plan to host the second P4G summit in June next year. P4G stands for Partnering for Green Growth and the Global Goals 2030, a public-private initiative to tackle climate change and other sustainable development challenges.

He had separate summit talks with his Polish, Danish and Australian counterparts, as well as UN Secretary-General Antonio Guterres and International Olympic Committee President Thomas Bach on the sidelines of the UN meeting.

Moon then attended a special event Tuesday to commemorate Mahatma Gandhi, an iconic figure in nonviolent resistance for freedom and peace.

He joined the ceremony to mark the 150th anniversary of Gandhi's birth at the invitation of Indian Prime Minister Narendra Modi. (Yonhap)