Moon did not immediately accept the invitation but said he hopes the "right conditions" will be created so it can go ahead.
A visit by Moon to the North would enable the first summit between leaders from the two Koreas since 2007, and would mark only the third inter-Korean summit to take place.
South Korean President Moon Jae-in has been using the Games in his efforts to re-engage with the North and to pave the way for talks over the North's weapons programme.
Trump has at times questioned the goal of further talks with the North after years of negotiations by previous US administrations failed to halt the North's weapons programs.
In an interview aboard Air Force Two on the way home from the Winter Olympics in PyeongChang, U.S. Vice President Mike Pence told The Washington Post that the administration of President Donald Trump would be open to possible talks with the North.
Pence is viewing the short-track competition, in which eight Americans are participating. Jo Yong Sam, department director general of North Korea's foreign ministry, said Thursday the country had never "begged the USA for dialogue" and wasn't about to start now.
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An Obama-era grant program that focused on fixing environmental problems and reducing energy dependence will also be cut. But the fund would match investments only up to $0.20 on the dollar at the maximum level of federal investment.
In the interview with the Washington Post published on Sunday, Pence said the USA agreed that diplomatic talks with North Korea would first be conducted by Seoul, after which direct talks with Washington may follow.
The North is showing no intention of scrapping its nuclear weapons and missile programs, and joint U.S.
The latest show of cooperation is a surprising invitation to the North Korean capital Pyongyang that leader Kim Jong-un offered to South Korean President Moon Jae-in.
Pence and Moon worked this out during their bilateral meeting Thursday at the Blue House and their joint viewing of speed-skating heats in Pyeongchang on Saturday evening.
Mr Mattis also said he doubted that the sporting rapprochement would undermine US-South Korean ties.
At the opening ceremony for the Games, Mr Pence, Kim Yo-jong and Kim Yong-nam were seated in close proximity to each other.
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In a statement, he thanked the voters and appealed for calm in celebrating the victory. Neither President nor Prime Minister commented on the results.
The discussions from Saturday's meeting weren't immediately released.
"It's not realistic to say we are only going to talk if you come to the table ready to give up your program", Tillerson told the Atlantic Council-Korea Foundation Forum in Washington DC.
The officials toasted with the Korean liquor "soju" and were served buckwheat and potato pancakes, dried pollock soup, grilled halibut and other dishes.
Yo-jong's visit to the South was the first visit by a member of the ruling Kim family ever since the Korean War ended in 1953.
After years of ineffective implementation, those sanctions may have begun to finally bite, which, according to a Japanese government official and experts, helps explain why Kim Jong-un agreed to send a national team and his sister to the Olympics.
Mr Pence stayed seated when South and North Korean athletes marched together under a unified flag, and also skipped a dinner with the North Korean delegation.
According to sources knowledgeable about Japan-U.S. ties, immediately after Abe met with Moon on February 9, U.S. officials requested and were granted a hurriedly called meeting between Abe and U.S. Vice President Mike Pence, who was also in Pyeongchang to take in the Opening Ceremony.
It's unclear whether the occasion could be used to set up bigger meetings between the Koreas to ease tensions.
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However, it is unlikely that Padmaavat can overtake Aamir Khan-starrer Dhoom 3 which is next in line with Rs 280.25 crores. India biz.' After the film saw a lull collection on Friday, people expected the buzz of Padmaavat to have fizzled out.
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