Modi expressed appreciation to the Republic of Korea government for facilitating supplies and transport of medical equipment being sourced by Indian companies, an official statement said.
South Korea's tally of cases of coronavirus cases rose to 977, fuelling fears the outbreak, which is thought to have begun in the central Chinese city of Wuhan in December, is developing into a pandemic.
Moon said U.S. President Donald Trump's recent letter to North Korean leader Kim Jong Un was a good sign that underscores his commitment to negotiations. Moon was speaking at a news conference at the presidential Blue House.
Ties between Seoul and Tokyo -- both of them US allies facing the twin challenges of nuclear-armed North Korea and an increasingly assertive China -- are at rock-bottom over a dispute related to Japan's use of forced labour during World War II, with the countries trading retaliatory sanctions.
Trump and Moon, in the Oval Office, discussed the possibility of Moon having an inter-Korean summit with Kim soon as a way to boost dialogue between the United States and North Korea on denuclearization.
The two leaders are expected to discuss stalled talks between the United States and North Korea after the second summit between Trump and North Korean leader Kim Jong Un broke down in late February, Yonhap reported.
A second summit between U.S. President Donald Trump and North Korean leader Kim Jong Un collapsed on Thursday over sanctions against Pyongyang. The two sides gave conflicting accounts of what happened, raising questions about the future of their denuclearisation negotiations.
Press Secretary Sarah Sanders told reporters traveling with Trump on Air Force One that he spoke for around 15 minutes each with Japanese Prime Minister Shinzo Abe and South Korean President Moon Jae-in.
The prime minister will arrive in Seoul on February 21 on a visit that will provide an important occasion for the two leaders to review the recent developments in bilateral relations, the Ministry of External Affairs said in a statement.
Moon made the comment when asked by reporters during a state visit to New Zealand about the likely timing of a possible trip to Seoul by Kim, who held summits with Moon and U.S. President Donald Trump this year.
"Modi jackets" are basically a vest-like sleeveless jacket the leader (Modi) usually dons, state-run Yonhap news agency reported.
Kim and U.S. President Donald Trump pledged to work towards denuclearisation at their landmark June summit in Singapore, but the agreement was short on specifics. Negotiations have made little headway since, with the North refusing to declare its nuclear weapons and facilities or agree to a concrete timeline.
"He said he hoped (U.S. Secretary of State) Mike Pompeo would visit North Korea soon, and also a second summit with Trump would take place in the near future, in order to move the denuclearisation process along quickly," Moon said.
Their trip to the mountain on the North Korean-Chinese border, and the striking photo-op that will resonate in both Koreas, followed a day of wide-ranging agreements they trumpeted as a major step toward peace.
Kim welcomed his visitor at Pyongyang's international airport -- where he had supervised missile launches last year as tensions mounted -- the two leaders of the divided Korean Peninsula embracing after Moon walked down the steps of his aircraft.
Moon said he hoped for speedy progress in talks between North Korea and the United States to achieve Pyongyang's complete denuclearisation.
The two Koreas agreed earlier this week to hold a third meeting between Moon and North Korean leader Kim Jong Un in September.
The Ministry of External Affairs said Indian PM Narendra Modi and Moon will deliberate on bilateral, regional and global issues of mutual interest.
The North, which invaded its neighbour in 1950, has yet to make any public pledge to give up its weapons, despite a rapid thaw in relations on and around the peninsula brokered by the South's President Moon Jae-in.
Linking the transport infrastructure of the two countries would give trade-dependent South Korea -- the world's 11th-largest economy -- a land route to the markets of China, Russia and on to Europe.
The reunions - scheduled for Aug. 20 to Aug. 26 - are an emotive issue, especially for the elderly relatives taking part in tearful meetings after decades of separation - and have taken place from time to time during periods of good ties between the two Koreas.
Moon and North Korean leader Kim Jong Un held a surprise meeting on Saturday at the border village of Panmunjom, during which they agreed that a North Korea-U.S. summit must be held.
Despite repeated references to "denuclearization of the Korean Peninsula" by the North, it remains unclear whether Kim will ever agree to fully abandon his nuclear arsenal.
After weeks of warm words and diplomatic backslapping, Pyongyang abruptly threatened to pull out of the planned summit next month because of US demands for "unilateral nuclear abandonment", according to the North's official KCNA news agency.
Moon met with Kim Jong-un last week at a Korean border village during last week's inter-Korea summit. The two leaders agreed to end hostile acts against each other along their tense border, establish a liaison office and resume reunions of separated families.