Moon later added that there were no winners or losers in the election, as everyone would participate in the building of a new South Korea.
The new president received 41.08 percent of the vote in Tuesday's election, which was held earlier than planned due to the impeachment of the former President Park Geun-hye over a far-reaching corruption scandal.
Moon has already appointed South Jeolla Province Governor Lee Nak-yon as prime minister.
The new president has also reportedly offered Suh Hoon, a veteran intelligence official, to lead the nation's National Intelligence Service, and Im Jong-seok, who was Seoul Mayor Park Won-soon's vice mayor for political affairs, to serve as the presidential chief-of-staff.
The election of a new president took place amid heightened tensions surrounding North Korea's nuclear and missile tests. In view of this, Moon promised to do everything in his power to maintain peace on the Korean peninsula, and stated that he would be willing to travel to Washington, Being, Tokyo and even, if possible, to Pyongyang.
The new South Korean leader pledged to further strengthen the country's relationship with Washington and promised to solve the issue of the Terminal-High Altitude Area Defense (THAAD) deployed by the United States in South Korea through dialogue with both Washington and Beijing. The latter recently spoke against the deployment of the system and urged the United States and South Korea to stop it.
According to the Yonhap news agency, Moon had already been briefed by Gen. Lee Soon-Jin, the chairman of the Joint Chiefs of Staff, on the state of the country's armed forces.
Lee reportedly told the president that South Korean forces were ready to act if provoked by the enemy.