The apparent difference between the two was displayed as the South Korean leader hosted Ivanka and other U.S. delegates for dinner at his office Cheong Wa Dae.
"On the other hand, active dialogue is being held between the South and the North amid the North's participation in the Olympics and this is greatly contributing to easing tension on the Korean Peninsula and improving the South-North relationship," Moon said, shortly after expressing gratitude for U.S. President Donald Trump's support for the PyeongChang Olympic Games.
"I believe this too was possible because President Trump strongly supports South-North Korean dialogue," he added.
Ivanka thanked Moon and his wife, Kim Jung-sook, for their warm welcome and hospitality, but said her trip was partly aimed at reaffirming the allies' commitment to "maximum pressure" against the North.
"I thank you for hosting us all here tonight as we reaffirm our bonds of friendship, of cooperation, of partnership and reaffirm our commitment to our maximum pressure campaign to ensure that the Korean Peninsula is denuclearized," she said.
In a separate meeting held before dinner, the South Korean president said the allies' joint efforts to denuclearize North Korea have failed so far.
"While noting that the dialogue for the denuclearization of the Korean Peninsula and the dialogue between the South and the North cannot go separate ways, the president said the two tracks of dialogue must move forward side by side and that it is important for South Korea and the U.S. to closely work together to that end," Moon's chief press secretary Yoon Young-chan told a press briefing.
"The country with the strongest determination to disallow North Korean nuclear weapons is South Korea. But the joint efforts of South Korea and the United States to denuclearize the Korean Peninsula over the past 25 years have not succeeded," Moon was quoted as telling Ivanka.
"The two countries must seize this hard-earned opportunity and I hope to realize such a historical achievement together with President Trump," he added.
Ivanka insisted the countries' maximum pressure campaign has led to positive outcomes, saying her country supports South Korea's efforts to put pressure on the North, according to Yoon.
Seoul and Pyongyang held three rounds of talks last month that eventually led to the North's decision to take part in the ongoing Winter Olympic Games in South Korea.
Moon has repeatedly stressed the need to build on the recent rapprochement between the two Koreas so they may spur a resumption of negotiations with the communist North to peacefully end its nuclear ambition.
Such negotiations require talks between Washington and Pyongyang, he has noted.
The White House earlier said Vice President Mike Pence was scheduled to meet North Korea's delegates to the opening ceremony of the PyeongChang Olympics in Seoul, but the North Koreans pulled out of the meeting at the last minute.
North Korea is sending another high-level delegation to the closing of the Olympic Games.
Ivanka, who arrived here earlier in the day, apparently had no plans to meet North Koreans while here.
"We are very excited to attend the 2018 Winter Olympic Games to cheer for Team USA and to reaffirm our strong and enduring commitment with the people of the Republic of Korea," she told reporters after arriving at Seoul's Incheon International Airport. Ivanka currently serves as a special adviser to her father. By the Yonhap.