Pyeongchang, South Korea (CNN) South Korean President Moon Jae-in said Saturday it was too early to talk about hosting a summit with North Korean leader Kim Jong Un, hinting he would not rush the matter.

A high-level delegation from the North invited Moon to Pyongyang for talks with his North Korean counterpart while in South Korea last week for the opening of the Winter Olympics in Pyeongchang.

The delegation's unprecedented visit was hailed in some quarters as a diplomatic breakthrough , but Moon must now chart a way through tricky diplomatic waters.

"There are high expectations and our hearts seem to be getting impatient. It is like the old saying, seeking a scorched-rice water from a well," Moon told journalists in Pyeongchang after being asked whether he planned to hold a summit with North Korea.

The proverb translates to rushing into something without fully understanding the consequences.

At the time of the invitation, Moon responded by suggesting the two countries "should accomplish this by creating the right conditions," according to a presidential spokesman.

Addressing journalists Saturday at the Games' main press center, Moon hailed the progress that had already been made in advancing inter-Korean talks.

"I hope that this will lead to an improvement in inter-Korean relations -- not only inter-Korean relations, but we also believe that there has been slowly, but gradually, a growing consensus on the need for dialogue between the United States and North Korea," he said.

"We hope that the dialogue between the two Koreas will be able to lead to dialogue between the United States and North Korea, and eventually denuclearization."

South Korea's government is "waiting on ongoing dialogue between South and North Korea to lead to talks between the US and North Korea," he added.

Moon said that the participation of North Korea had helped to make it "a very safe Winter Olympic Games" after a period of mounting tensions on the Korean Peninsula.

People in the Koreas and around the world had been moved to see a unified South-North Korea team compete, he added.

If an encounter in Pyongyang took place, it would be the first between Kim and a South Korean leader. It would also be the first North-South summit on the peninsula since 2007 when South Korean President Roh Moo-hyun -- in whose administration Moon served -- met with Kim's father, Kim Jong Il.

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While the meeting would be a diplomatic coup for Moon -- whose decision to pursue warmer relations with the North stands in stark contrast with his conservative predecessor -- it could strain relations with the United States, which appeared uncomfortable at the warm welcome afforded to the North Korean delegation.

US Secretary of State Rex Tillerson said Monday it will be "up to North Korea" to decide when it is ready to engage in serious and meaningful diplomatic talks with the United States.

Tillerson was reacting to Vice President Mike Pence's remarks to The Washington Post a day earlier that the Trump administration is willing to sit down and talk with North Korea.

Pence on Wednesday told US news outlet Axios that he actively chose to ignore Kim's sister at the Games' opening ceremony to send a "very clear message" to North Korea over its nuclear weapons threat.

"The fixed policy of the United States of America is that we are going to continue with all options on the table to bring intensifying economic and diplomatic pressure to bear until North Korea, once and for all, completely and verifiably abandons its nuclear weapons and ballistic missile program," Pence is reported to have said.