Chinese State Councilor Yang Jiechi and U.S. Secretary of State Rex Tillerson exchanged views on the situation on the Korean Peninsula via phone on Sunday.
The talk came after the Democratic People's Republic of Korea had reportedly fired an unidentified missile early on Sunday from its eastern coastal city of Sinpo.
But the missile was believed to have exploded on launch, according to South Korea's Joint Chiefs of Staff.
Yang and Tillerson also discussed the implementation of those agreements reached by the two countries' presidents during their first meeting in the U.S. state of Florida earlier this month.
The successful meeting between Chinese President Xi Jinping and U.S. President Donald Trump at the Mar-a-Lago estate has set a constructive tone, defined the direction and made a plan for the development of bilateral ties, Yang told Tillerson, noting that the two leaders also held a good phone conversation just a few days ago.
For the next stage, the two sides should make joint efforts, in accordance with the spirit and consensus reached in the two heads of state's meeting and phone conversation, to strengthen high-level exchanges and dialogues and expand mutually beneficial cooperation, Yang said.
China and the United States should manage their differences on the basis of mutual respect and promote greater development of bilateral ties, so as to better serve the two peoples and peoples of the world, he added.
For his part, Tillerson noted that the two presidents' meeting at Mar-a-Lago and the phone conversation are positive and fruitful.
The United States looks forward to enhancing communication with China, preparing for the next stage's high-level exchanges and dialogues, and jointly pushing forward bilateral relations, said Tillerson.
Xi and Trump met in Florida on April 6 and 7, the first face-to-face communication between the Chinese and U.S. heads of state since the new U.S. administration took office.
The pair on Wednesday held a telephone conversation to discuss the situation on the Korean Peninsula and in Syria.