Kim Jong Un and Moon Jae-in said they agreed to turn the Korean peninsula into a "land of peace without nuclear weapons and nuclear threats".
It will be Pompeo's fourth trip this year aimed at persuading North Korea to abandon a nuclear weapons programme.
Sergei Lavrov was the first Russian official to be received by Kim Jong Un, Russian news agencies said.
North Korea's Kim Yong Chol, vice chairman of the ruling Workers' Party's Central Committee, was scheduled to fly to the United States on Wednesday.
Qatar expressed hope that the historic summit between the leaders of South Korea and North Korea will open the door for communication between the peoples of the two countries and achieve lasting peace and stability.
Israeli Prime Minister Benjamin Netanyahu said that Iran had lied about never having pursued nuclear weapons and had continued to preserve and expand its nuclear weapons knowledge even after signing a 2015 deal with global powers.
Moon Jae-in and North Korean leader Kim Jong Un pledged at a summit to end hostilities between their countries and work toward the "complete denuclearisation" of the Korean peninsula. Trump is preparing for his own summit with Kim.
Iran's armed forces spokesman said on Saturday that there can be no talks on the country's missile programme without the West's destruction of its nuclear weapons and long-range missiles.
UN Secretary General Antonio Guterres called on Monday for a new global effort to get rid of nuclear weapons but said many states still wrongly think they make the world safer.
The Pyeongchang Games have become a venue for geopolitics as much as sports as the nuclear-armed North mounts a charm offensive.