Moon favours engagement with Pyongyang to bring it to the negotiating table, unlike his conservative predecessors and the US Trump administration, which backs stronger sanctions and has threatened military action.
"We urge the relevant authorities to immediately detect and arrest and hand over to the DPRK the masterminds of the disgusting state-sponsored crime, accomplices and their followers", the office said, referring to the country by the initials of its official name, the Democratic People's Republic of Korea.
Beijing has asked the deployment be canceled because of THAAD's powerful radar and regional surveillance capabilities.
"The United States put THAAD in there as part of their "pivot against China" that was started by [previous USA president Barack] Obama".
Japan's Foreign Minister Fumio Kishida said in an Upper House committee meeting on Thursday that he was eager to call on Moon to jointly step up pressure on the DPRK and said that a multilateral approach was the best way to deal with the DPRK's provocations.
China has rigorously objected to the deployment of the U.S. missile defense system in South Korea, saying it destabilized regional security and did little to curb any threat from North Korea's nuclear and missile programs, which are in defiance of USA pressure and United Nations sanctions.
Moon's pick for National Intelligence Service chief is Suh Hoon, a longtime intelligence official Moon said would be the right man to push reforms at NIS, which has always been accused of meddling in domestic politics.
Moon had a 40-minute conversation with Chinese leader Xi Jinping, his spokesman Yoon Young-Chan told reporters, with the two agreeing denuclearising Pyongyang was a "common goal" between them.
You play finals to win! - Ajax boss Bosz wants to make history
Ajax , who reached the final with a 5-4 aggregate win, have also been charged over "acts of damage" during Thursday's match. In the Europa League, Ajax topped their group without losing a game, then beat Legia Warsaw, Copenhagen, Schalke and Lyon .
South Korean activists hold a banner during a rally against the plan to deploy the USA -built Terminal High Altitude Area Defense, near the US embassy in Seoul, July 11, 2016.
Japan is still at odds with South Korea over "comfort women" statues erected to memorialize the women coerced into sexual slavery by the Imperial Japanese Army during the war.
The two sides agreed on the importance of denuclearizing the peninsula.
Moon Jae-in's victory in the South Korean presidential election bodes well for East Asia in general and the Korean peninsula in particular.
Moon Jae-in emerged the victor in the May 9 presidential election to have collected 41.1% of the votes. China denies it has done anything to hurt South Korean businesses.
"On security: There are still many unknowns about how Moon's more conciliatory tone with North Korea will pan out", she said.
Mr Moon's office said the new president also spoke with Vladimir Putin on Friday - with the Russian leader pledging to play a constructive role in resolving the North Korea crisis.