The document's existence was first mentioned by White House national security advisor John Bolton in television interviews he gave after the two-day summit. Bolton did not disclose in those interviews the pivotal U.S. expectation contained in the document that North Korea should transfer its nuclear weapons and fissile material to the United States.
The document appeared to represent Bolton's long-held and hardline "Libya model" of denuclearization that North Korea has rejected repeatedly. It probably would have been seen by Kim as insulting and provocative, analysts said.
Trump had previously distanced himself in public comments from Bolton's approach and said a "Libya model" would be employed only if a deal could not be reached.
The idea of North Korea handing over its weapons was first proposed by Bolton in 2004. He revived the proposal last year when Trump named him as national security advisor.
The document was meant to provide the North Koreans with a clear and concise definition of what the United States meant by "final, fully verifiable, denuclearization," the source familiar with discussions said.
The White House did not immediately respond to a request for comment. The State Department declined to comment on what would be a classified document.
After the summit, a North Korean official accused Bolton and Secretary of State Mike Pompeo of "gangster-like" demands, saying Pyongyang was considering suspending talks with the United States and may rethink its self-imposed ban on missile and nuclear tests.
The English version of the document, seen by Reuters, called for "fully dismantling North Korea's nuclear infrastructure, chemical and biological warfare program and related dual-use capabilities; and ballistic missiles, launchers, and associated facilities."
Aside from the call for the transfer of Pyongyang's nuclear weapons and bomb fuel, the document had four other key points.
It called on North Korea to provide a comprehensive declaration of its nuclear program and full access to U.S. and international inspectors; to halt all related activities and construction of any new facilities; to eliminate all nuclear infrastructure; and to transition all nuclear program scientists and technicians to commercial activities.
The summit in Vietnam's capital was cut short after Trump and Kim failed to reach a deal on the extent of economic sanctions relief for North Korea in exchange for its steps to give up its nuclear program.
The first summit between Trump and Kim, which took place in Singapore in June 2018, was almost called off after the North Koreans rejected Bolton's repeated demands for it to follow a denuclearization model under which components of Libya's nuclear program were shipped to the United States in 2004.
Seven years after a denuclearization agreement was reached between the United States and Libya's leader, Muammar Gaddafi, the United States took part in a NATO-led military operation against his government and he was overthrown by rebels and killed.