President Donald Trump says the US will only talk to North Korea "under the right conditions".
Ivanka made the remarks as she before boarding a plane back to the USA at the Incheon International Airport, west of Seoul.
Moon met Kim in Pyeongchang, where the Olympics were held, before the closing ceremony, the South Korean government said. "Thanks for the warm hospitality".
"We will see if Pyongyang's message today, that it is willing to hold talks, represents the first steps along the path to denuclearization", it said.
The Trump administration has been in contact with North Korean officials via the North's United Nations representative in NY and other diplomatic channels. Though Pence stood to cheer the entrance of the USA team, he remained seated when athletes from North and South Korea marched together behind a "unification" flag, leaving Moon to instinctively turn around and shake Kim's sister's hand.
For the opening ceremony, the North sent Kim Yo Jong, the younger sister of North Korean leader Kim Jong Un. "They also discussed the continued effort on the joint maximum pressure campaign against North Korea", a senior administration official said in a statement to CNN.
Facebook: Trump campaign paid more for ads than Clinton campaign
Parscale began working for the Trump Organization in 2011, on website design and digital media issues for Trump's businesses. Trump is big on loyalty (although it often runs one way) and hasn't always gotten it from his campaign managers.
Earlier, the USA said the worldwide community needs to maintain maximum pressure on North Korea until it gives up its nuclear weapons development.
A powerful North Korean general this morning wrapped up his visit to the South as part of an Olympics charm offensive by Pyongyang that has drawn angry protests calling for his arrest. Earlier in the day, reports Reuters, a statement released on state media accused the United States of stoking war on the Korean peninsula with Friday's announcement of sanctions.
It was not clear if the wording signaled a departure from Washington's long-held position that North Korea must take concrete steps toward disarming before talks can begin.
According to the U.S., a planned meeting between the delegations from Washington and Pyongyang the following day was cancelled at short notice by the North Koreans. "I ask China to actively support dialogue between the South and North Korea to denuclearize the Korean Peninsula and also establish peace, as well as dialogue between the North and the United States for such goals", the president said.
Several conservative lawmakers protested on a road near the inter-Korean land border on Tuesday, demanding Kim apologize over the attacks before leaving.
But he must first strike a balance with Washington, which has a policy meant to isolate and sanction the North until it agrees to give up its nukes.
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