Vietnam and the United States had advanced ties to a new level under the Obama administration amid a dispute with China over East Vietnam Sea issues, while Trump has also expressed his hope for a stronger relationship.
Trump sent a letter to Quang "affirming his wishes to promote cooperation on economics, trade, regional and international issues", the Vietnamese government website said.
Quang made the remarks during a meeting with the U.S. ambassador to Vietnam on Friday.
Quang emphasized that Vietnam welcomes U.S. efforts to improve cooperation with countries in the region to maintain the freedom of navigation and aviation.
U.S. Ambassador Ted Osius was reported as saying that Trump is considering attending the upcoming Asia-Pacific Economic Cooperation (APEC) summit in Vietnam this year.
Vietnam had been expected to be one of the biggest beneficiaries of the Trans Pacific Partnership (TPP) free trade deal which Trump pulled the U.S. out of in January, but Hanoi has also been building links with the United States amid a maritime dispute with China.
China claims most of the East Vietnam Sea, while Taiwan, Malaysia, Vietnam, the Philippines and Brunei claim parts of the sea that commands strategic sea lanes and has rich fishing grounds along with oil and gas deposits.
Prime Minister Nguyen Xuan Phuc said last month he was ready to visit the United States to promote ties, particularly trade.