Pyongyang has had more than its usual share of criticism for Washington in recent months.
Caught between the USA and China, Moon will try to pursue an independent foreign policy.
Moon's election could add volatility to relations with Washington, given his questioning of the Thaad deployment, but it was not expected to change the alliance significantly, a U.S. official said.
Pyongyang's relations with Moon's conservative predecessor, Park Geun-hye, were extremely bad, but even so, the North is nearly certain to be cautious about any Moon proposals for increased engagement.
Mr Moon told President Xi Jinping that North Korean provocations had to stop before the deployment of the Terminal High Altitude Area Defence (Thaad) system could be reconsidered.
Economically, Xinhua argues, South Korea should look to Beijing and not Washington for expanded opportunity: "With China being the country's largest trading partner and a major source of its trade surplus, it is apparently desirable for the new South Korean leader to join hands with China and work for constant improvement in their ties".
A North Korean parliamentary committee sent a rare letter of protest to the U.S. House of Representatives on Friday over its new package of tougher sanctions. Out of 32.8 million votes cast on Election Day and during a two-day early voting period last week, Moon received 41.08 percent, or 13.4 million, of votes cast, handily clinching the office he had failed to win in 2012.
The decision by the ousted Park's government to host the Thaad system has already proved a headache for Moon as Seoul tries to walk a fine line between Washington, its closest security ally, and Beijing.
This runs directly contrary to Mr Trump's policy of tightening economic sanctions against the North and even threatening military action to force Pyongyang to abandon its nuclear weapons programme.
But challenging Washington on THAAD would be hard for Moon, despite widespread opposition to it in South Korea - especially after Trump suggested South Korea should pay the roughly $1 billion bill for it - and loud protests from China, which claims the system is a security threat.
Moon has long said the next South Korean government should review the Thaad deployment and decide to allow it only after seeking China's understanding.
He also pledged to strengthen South Korea's alliance with the US.
"I take this office empty-handed, and I will leave the office empty-handed", Moon said. China and Russian Federation have also criticized the deployment of THAAD, saying it would significantly affect the balance of power in the region and would lead to more instability.
China sees it as a threat to its security and has called for its withdrawal, but has also denied it was doing anything to retaliate against South Korean businesses. Chinese group tours to South Korea have also been canceled, while anti-Korean sentiment has proliferated online. The nuclear issue is now central to inter-Korean relations.
Separately, the CIA said on Wednesday it had established a Korea Mission Center to "harness the full resources, capabilities, and authorities of the agency in addressing the nuclear and ballistic missile threat posed by North Korea". Moon opposes a 2015 agreement signed by Park that was heralded as a final settlement for Korean women who were among many sexually enslaved in Japanese military brothels before and during World War II.
Historical issues should be overcome "wisely" and not hamper the countries' relationship or efforts to deal with the North, the Blue House quoted Moon as saying.
The South's president has also several times expressed interest in meeting the North's ruler Kim Jong-un, and the reclusive state's ruling party newspaper said Thursday the two Koreas should "seek dialogue and negotiations at various levels".
Mr Moon was sworn in on Wednesday.