Sending Trump the sincere regards of Chinese President Xi Jinping, Yang said the two nations should manage and control their disputes and sensitive issues properly, and implement the consensus reached by Trump and Xi during their meeting last November in Beijing.
The two presidents agreed during their Beijing meeting that China and the United States have wide-ranging common interests and the significant responsibilities of securing world peace, prosperity and stability, Yang said.
He further said China-US ties have global relevance, and promoting the bilateral relationship is not only in line with the fundamental interests of the two peoples, but also meets the common aspirations of international society.
Yang said Xi and Trump have mapped out the future direction of bilateral efforts in their close contacts via telephone calls and letters, in which the two top leaders said they wanted to accelerate bilateral cooperation in multiple areas.
He added that the two sides are expected to maintain close communication at all levels, host the second round of the four high-level dialogue channels on the fronts of diplomacy and security, law enforcement and cyber security, social and cultural issues as well as economy.
The senior Chinese official also urged the two nations to expand their cooperation in economy and trade, military, law enforcement, drug control and people-to-people exchanges, among other areas.
For his part, Trump conveyed his sincere regards to Xi, saying US-China relations are very important, and Washington is willing to strengthen cooperation with Beijing to further promote bilateral ties.
Saying his state visit last November to China was a huge success, Trump said he agreed the two sides should fully implement the consensus he had reached with Xi during their meeting in Beijing.
On the same day, Yang also met with US National Security Adviser H. R. McMaster and senior White House adviser Jared Kushner to exchange ideas on promoting China-US cooperation on bilateral, regional and international issues.
The senior Chinese official is on a two-day visit to Washington at the invitation of US Secretary of State Rex Tillerson. The two top-level diplomats met on Thursday and reached consensus on holding the four dialogue channels this year to make a bigger cake of cooperation in the economic and trade areas.
Yang urged global support for inter-Korean rapport and the continued easing of tensions on the Korean Peninsula during the meeting.
For his part, Tillerson reiterated the US commitment to the one-China policy, in response to Yang's request that the US side should take China's concerns regarding the Taiwan issue seriously.
After a year of steady development in China-US ties, boosted by successful face-to-face meetings and frequent phone conversations between Xi and Trump, bilateral relations have been facing several challenges since the end of 2017 after some worrisome moves on Washington's part.
In addition, Washington has maintained its so-called "maximum pressure" campaign against Pyongyang, yet so far the strategy has not achieved the expected results.