During Wednesday's conversation, Vietnamese premier Nguyen Xuan Phuc congratulated Trump on his election win and stressed the importance of maintaining friendship and cooperation.
"President-elect Trump spoke highly of the achievements of Vietnam, as well as the positive developments in bilateral ties," Vietnam's government said on its news website, Reuters reported.
"He also asserted his wish to cooperate with Vietnam to accelerate the relationship between the two countries."
Trump has had conversations with several leaders of countries locked in maritime disputes with China, among them Japan, the Philippines and Taiwan.
His trade platform runs counter to Vietnam's interests, however, with his opposition to a Trans-Pacific Partnership proving a major setback for Southeast Asia's biggest exporter to the United States.
Trump and Phuc discussed ways to promote economic ties, trade and investment, the government added.
In a statement, Trump's transition team confirmed the conversation, saying the two men "discussed a range of shared interests and agreed to work together to continue strengthening the relationship between the two nations".
Just days after Trump's win, Phuc told parliament that ratification of the TPP would be shelved because of political changes in the United States, but Vietnam still wanted good relations with Washington.
In a separate development, a US guided-missile destroyer, the Mustin, visited Cam Ranh international port on Thursday in a routine technical stop, the US embassy said.
The ship's visit was "an example of the depth of our comprehensive partnership and the importance of strengthening our civilian and military ties," said US Ambassador Ted Osius.