Observers say the document lacks substance, in particular on how denuclearisation would be achieved.
"For the record of history, never before has a U.S. President spoken this way of a dictator accused of crimes against his own people", former Rep. David Jolly (R-Fla.), a frequent critic of the president, wrote on Twitter.
The historic agreement came after the two leaders held several meetings throughout the day.
In November 2017, after returning to Washington from a 12-day, five-nation trip to Asia, President Trump stood in the Diplomatic Reception Room of the White House and insisted that he and President Xi had agreed they "would not accept a so-called "freeze for freeze" agreement like those that have consistently failed in the past".
Japan, the chief USA ally in the region, got none of what it wanted - Kim made no promise to address the issue of Japanese citizens abducted by North Korea, and he offered no limits on his ballistic missile programs.
"I think he loved it", Mr Trump said, referring to Mr Kim.
The Federal Government has applauded the outcome of the Tuesday's Summit between U. S. President Donald Trump and Chairman Kim Jong Un of Democratic People's Republic of Korea (DPPK).
Two years ago Barack Obama travelled to Cuba - and was roundly denounced by conservatives for breaking bread with totalitarian leaders and praised by liberals for his statesmanship. "I hope it's going to be soon", he said Tuesday at an hour-long briefing. We fly in bombers from Guam... to practice and drop bombs all over the place and then go back to Guam.
The US maintains around 30,000 troops in South Korea and once a year it brings in others - typically from its Pacific base in Guam - to join large-scale drills.
"We would like to seek an understanding of this between Japan, the US and South Korea", Japan's defence minister, Itsunori Onodera, said.
Shaheen and other lawmakers added there should be no cancellation of USA military exercises in Asia, as Trump suggested, without first consulting South Korea and other allies in the region.
Democratic Senator Jeanne Shaheen said, "We can't lose sight of the fact that there are awful, horrific humanitarian issues in North Korea, human rights abuses".
"The issue's inclusion at the summit reflects the efforts of fierce lobbying by veterans groups in America, including Veterans of Foreign Wars, which wrote to Trump last week asking him to discuss the matter with Kim".
The KCNA report said Trump committed to ending the drills during his meeting with Kim. "I don't say he was nice".
Highlighting the continued differences in the two countries' views of the denuclearization process, the report also said that they had agreed on a "step-by-step" approach. "That's going to start very soon".
"I think, without Otto, this would not have happened", Trump told reporters.