Early results suggested that Moon, the Democratic Party's candidate in the election to replace ousted president Park Geun-hye.
Kim said that his meeting with Moon would serve as a "historic chance" for the Korean people, who want to see the strengthening of inter-Korean relations.
The vests gifted by Prime Minister Narendra Modi to South Korean President Moon Jae-in were 'Modi Jackets' and not traditional Nehru jackets as claimed by some, the company which makes them said.
'Much depends on Moon's persuasive skill to make both Trump and Kim shed some of their rigidity and be flexible to accommodate contrarian viewpoints,' says Dr Rajaram Panda.
Moon who is on a three-day visit to India arrived in New Delhi on Sunday evening.
The two leaders discussed the possible US-North Korea summit.
The historic peace talks are aimed at ending their decades-long conflict and come weeks before Kim is due to meet United States President Donald Trump.
Moon Jae-in hope that the summit will open a new era of complete denuclearisation, peace.
India has become world's 2nd largest mobile phone: Modi
South Korean President's office says Kim promised to close N Korea's nuclear test site next month.
South Korean president Moon Jae-in has backed Chung Hyeon to bring more joy to his country after the youngster's inspired charge at the Australian Open came to a heart-breaking end in the semi-finals on Friday.
Trump told reporters that US and South Korea are facing the threat of reckless and brutal regime of North Korea.
Moon Jae-in's visit will play a crucial role in exploring complementarities between India's Act East policy and South Korea's New Southern policy, says Dr Rahul Mishra.
The forthcoming summit would review the implementation of the inter-Korean summit agreement signed between the two countries during the first meeting in Panmunjom.
Modi held several bilateral and trilateral meetings with world leaders.
North Korea made its decision to pull out of Tokyo at a meeting of its Olympic committee and Sports Minister Kim Il Guk on March 25, the ministry said on its website.
PM indirectly referred to North Korea's proliferation linkages with Pakistan.
Spectacular IMAGES from the closing ceremony of the 2018 Winter Olympics held in Pyeongchang, South Korea
Trump and South Korean President Moon Jae-in are expected to discuss strengthening the alliance, developing close coordination to resolve the North Korea nuclear issue, establishing peace and prosperity in Northeast Asia, and increasing cooperation on bilateral and global issues.
The report of Kim's illness started doing rounds following his absence at the Kumsusan Palace of the Sun in Pyongyang on the birthday of late state founder and his grandfather, Kim Il-sung, earlier this month.
17 Republican lawmakers want Nobel for his work to end the Korean War.
KCNA said the new type of surface-to-ship cruise missile is designed to hit 'any enemy group of battleships' that threatened the country.
White House officials have been discussing sites as far-flung as Singapore and Mongolia for the planned meeting between Trump and Kim.
He praised the "very bold move" taken by China's central bank to stop financial transactions with North Korea.
The letter comes as the two sides negotiate details of a second meeting between the two leaders. It was flown to Pyongyang and delivered by hand, the CNN reported, quoting a source familiar with the ongoing talks between Washington and Pyongyang on denuclearisation of the Korean Peninsula.
The two Koreas have agreed to pursue a bid to co-host the 2032 Olympic Games, they said in a joint statement on Wednesday following a summit between North Korean leader Kim Jong Un and South Korean President Moon Jae-in.
The US president praised Kim as "very open" and "terrific", despite the glacial pace of progress toward denuclearisation on the Korean Peninsula.
On Sunday, North Korea said it detonated a hydrogen bomb designed for a long-range missile and called its sixth and most powerful nuclear test a "perfect success", sparking world condemnation and promises of tougher US sanctions.
After entering the Peace House for the inter-Korean summit, Kim wrote in the guest book 'a new history begins now'.
World leaders, including Modi, also inaugurated the Gandhi Solar Park at the UN headquarters here and released a commemorative stamp issued by the UN on the occasion of Gandhi's 150th birth anniversary.
Kim did not rule out diplomacy with the Biden administration despite that Pyongyang called Biden a 'rabid dog' after Biden labelled Kim a 'thug'.
North Korean have proven to be priceless when measured in diplomatic currency at South Korea's Winter Games
The MEA said Singh's visit to Pyongyang was at the invitation of North Korean government.
Trump and Kim are scheduled to meet in Singapore on June 12.
Pompeo would leave for New Delhi on June 24.
Japan's Mima Ito took the bronze medal after beating Han Ying of Germany in straight games.
The Winter Olympics sparked to life in a vivid, colourful ceremony of fire and ice in South Korea
The football teams will be competing amid a tense political backdrop with international negotiations stalled over North Korea's nuclear weapons and ballistic missiles.
North Korea will take part in the next two Olympic Games in Japan and China, International Olympic Committee President Thomas Bach said on Saturday after meeting North Korean leader Kim Jong Un in Pyongyang.
Modi will also meet Chinese President Xi on the sidelines of the summit. It would be their fourth meeting in last seven months.