The two leaders confirmed in phone talks on Wednesday night there would be "no meaningful dialogue" unless North Korea agreed on "complete, verifiable and irreversible denuclearization," the ministry said in its statement.
Kim Jong Un gave instructions for measures aimed at more inter-Korean engagement after his younger sister Kim Yo Jong led a three-day visit to the Pyeongchang Winter Olympics, North Korea's state media reported on Tuesday.
That provides a little more leverage for South Korea in its path-finding outreach to the North and could reduce potential strains in the US-South Korean alliance.
The state-run KCNA news agency published a short report on Kim meeting the delegation yesterday following its return to Pyongyang.
Bach has said that he would make the visit on the North's invitation as part of an agreement between the IOC and both North and South Korea.
Speaking to the Washington Post en route home from a five-day Asia trip, the president's second-in-command described the strategy as "maximum pressure and engagement."
That is the assessment of a former South Korean government minister and political experts who say the North has used the Games to drive a wedge between South Korea and its U.S. ally and to potentially ease pressure on its sanctions-crippled state.
North Korean leader Kim Jong Un's sister Kim Yo Jong and other North Korean officials are set to fly back to Pyongyang on Sunday night.
North Korean leader Kim Jong Un invited South Korean President Moon Jae-in to Pyongyang "at an early date", South Korean officials said on Saturday, potentially setting up the first meeting of Korean leaders in more than 10 years.
Kim Yo Jong flew into the South on her brother's private jet on Friday before she and other North Korean officials attended the opening ceremony of the Winter Olympics in the alpine resort town of Pyeongchang.
North Korea last year increased the pace of its missile programme. Since February, Pyongyang has fired off 23 missiles.
Pence shook hands with other leaders, including close ally Japanese Prime Minister Shinzo Abe, but not Kim Yong Nam, according to a Blue House pool report.
South Korea presented on Wednesday a request to the council's sanctions committee for an exemption to the travel ban imposed on Choe Hwi, chairman of North Korea's National Sports Guidance Committee.
Abe, set to meet South Korean President Moon Jae-in later on Friday, also said he would convey to Moon Tokyo's position on a 2015 bilateral agreement on "comfort women" - many Korean - who were forced to work in Japanese military brothels during World War Two, while urging "future-oriented" two-way ties.
"We ... have become capable of showcasing our stature as a world-class military power to the world.", Kim Jong Un said.
U.S. Vice President Mike Pence, who described North Korea as the world's most tyrannical regime on Wednesday, flies in to South Korea on Thursday ahead of the opening ceremony in the mountain resort of Pyeongchang, just 80 km (50 miles) from the heavily armed border with North Korea.
"We will continue to isolate North Korea until it abandons its nuclear and ballistic missile program once and for all.", US Vice President Mike Pence said.
The two leaders spoke over phone yesterday during which May also briefed Trump on her recent trip to China, the White House said.
Hundreds of angry South Korean conservatives demonstrated Tuesday as a ship from North Korea carrying around 120 performers arrived at the eastern port of Mukho.
It said the two leaders also agreed that a U.S.-Britain data sharing agreement would benefit both countries and that they would advocate for legislation together.
Washington has previously said it won't seek to initiate contact with North Koreans attending the South Korean games, but it does want talks with Kim Jong-Un in an effort to get him to abandon his nuclear program.
The Games opening ceremony will also be attended by U.S. Vice President Mike Pence, Japanese Prime Minister Shinzo Abe and other world leaders.
"North Korea sent emails that could hack into cryptocurrency exchanges and their customers' private information and stole (cryptocurrency) worth billions of won," said Kim Byung-kee, a member of South Korea's parliamentary intelligence committee.
Yonhap cited a South Korean lawmaker as saying the spy agency had told lawmakers it was working with foreign intelligence agencies to beef up foreign nationals' identity checks as an anti-terrorism plan for the Olympics.
The trip by Kim Yong-Nam will be the diplomatic high point of the rapprochement between the two Koreas triggered by the Pyeongchang Games in the South, which have their opening ceremony on Friday.