While Trump noted North Korea's nuclear issue is a hard problem - he said it can be resolved.
Trump wants to tighten an economic vise and has raised the possibility of military force as the North approaches the capability to threaten America with a nuclear-tipped missile.
"The new South Korean government will actively communicate with China on these issues and seek appropriate resolutions", the statement quoted Moon as saying.
But Abe also said "dialog for dialog's sake would be meaningless" and he called on North Korea to demonstrate "sincere and concrete action", Hagiuda said, adding that Moon shared Abe's views. Now more than ever is the time for Seoul to devote itself to balanced diplomacy with the position that it should take the initiative in resolving problems on the Korean Peninsula.
President Donald Trump on Wednesday invited South Korea's new president to visit the White House after an election victory that could cause friction between the allies over how to deal with North Korea's nuclear threat.
Relations between Seoul and Beijing have been growing sour amid the ongoing deployment of a US missile defense system in South Korea.
China says the Terminal High Altitude Area Defense (THAAD) undermines its security as its powerful radar can probe deep into its territory.
South Korean President Moon Jae-in and his Chinese counterpart Xi Jinping agreed Thursday to further improve their countries' bilateral relations, while jointly calling for efforts by all concerned parties to help denuclearize North Korea, Seoul's presidential office said.
Moon's plan to send a special envoy to China to resolve the THAAD issue and the North Korean nuclear issue is particularly significant.
China has engaged in economic retaliation against Korea over the deployment of the US -led Thaad antimissile system in Seongju County, North Gyeongsang, which it says goes against its security interests.
The official Korean Central News Agency (KCNA) put out a four-sentence report late on Thursday on Mr Moon, who calls for dialogue, along with sanctions and pressure, to curb the North's nuclear ambitions.
South Korea and the United States began deploying the THAAD system in March and it has since become operational.
Xi explained the reasons for Beijing's strong and repeated opposition against the THAAD deployment, according to Yoon.
Mexican President Enrique Peña Nieto also sent his congratulations to South Korea's new president via Twitter.