The United States' secretary of state on Thursday met with the South Korean president in Seoul to discuss the outcome of the historic summit between the US president and the North Korean leader.

According to the South Korean presidential office, Mike Pompeo told South Korean president Moon Jae-in at the start of the meeting that there is still "a great deal of work to do" and that he trusts that both sides will be able to cooperate and bring peace to the Korean Peninsula.

Donald Trump and Kim Jong-un signed an agreement at the end of their summit on Tuesday in which they pledged to open a new chapter of relations, establish peace and work towards North Korea's complete denuclearization.

The US Secretary of State said he was "confident that we took a very good, significant step in Singapore" and that the US and North Korea will work together to provide their citizens with the best results.

Pompeo thanked the South Korean president, who has met with Kim Jong-un twice since April, for his mediation between North Korea and the US, saying that if it had not been for Moon's effort, the talks between Trump and Kim on Jun. 12 would not have been possible.

Moon said he was satisfied with the outcome of the summit and what is most important is that it has allowed the world to escape from threats of a nuclear war and long-range missiles.

There was no mention of the suspension of annual South Korean-US military maneuvers, which Trump unexpectedly announced on Tuesday at the end of the summit.

Pompeo is scheduled to meet on Thursday in Seoul with his South Korean and Japanese counterparts Kang Kyung-wha and Taro Kono to further discuss the details of the Singapore summit.