At one of Quang's last appearances, during a visit to Hanoi by Indonesian President Joko Widodo on September 11, the president appeared visibly unwell and stumbled as he stepped on to a platform to inspect a guard of honour.
Vietnam Television reported he suffered from a "serious illness despite efforts by domestic and global doctors and professors".
"His hosting of President Donald J. Trump's historic state visit to Hanoi in November 2017 helped advance the U.S. -Vietnam Comprehensive Partnership to new heights on the basis of mutual understanding, shared interests, and a common desire to promote peace, co-operation, prosperity, and security in the Indo-Pacific region", he said in a statement posted on the embassy's website.
Mr Quang was one of Vietnam's top three leaders - Vietnam has no paramount ruler and is also led by the prime minister and Communist Party chief.
Mr Quang had been serving as president since April 2016.
HANOI, VIETNAM-Vietnamese President Tran Dai Quang, the country's No. 2 after the ruling Communist Party's leader, died Friday after a serious illness, the government said.
Quang was from Quang Thien Commune, Kim Son District, Ninh Binh Province in northern Vietnam.
At an APEC meeting in Danang in November past year, he hosted a group of world leaders, including US President Donald Trump and China's Xi Jinping.
"More than anyone else, he's responsible for the ministry of public security's expansion into all aspects of daily Vietnamese life, bringing all the rights abuses, corruption and extortion that come with increased police presence", he added.
Quang was appointed to the role in April, 2016.
His time in office was dominated by a simmering conflict with Beijing over the South China Sea, a long-running dispute between the communist neighbours that escalated on several occasions.
As president, he oversaw a crackdown on dissidents that rights groups have decried as a chokehold on free expression.
Funeral arrangements were not immediately announced.