US President Donald Trump has said sanctions would remain on North Korea for now, but he wants to remove them as soon as possible.
He was speaking after a historic first meeting with North Korean leader Kim Jong Un at their summit in Singapore.
"The sanctions will come off when we are sure that the nukes are no longer a factor. I hope it is soon ... at a certain point, I look forward to taking them off."
Mr Trump said Mr Kim committed to destroying a weapons testing facility. The US President also said North Korea would destroy a "major" missile engine test site, but did not elaborate.
At the summit, the leaders signed a "comprehensive" document aimed at the denuclearisation of the Korean peninsula.
Mr Trump said he expected the denuclearisation process to start "very, very quickly".
The establishment of "new US-DPRK relations" is also envisaged as is a commitment by the US to "security guarantees".
He also said the US will stop holding military exercises on the Korean peninsula. Washington and Seoul are security allies and hold joint exercises every year that infuriate Pyongyang.
"We will be stopping the war games, which will save us a tremendous amount of money," Mr Trump told reporters, adding that "at some point" he wanted to withdraw US troops from the South.
Mr Trump said he had raised the issue of human rights with Mr Kim. "We did discuss it today, strongly," he said.
"We will be doing something on it. It's rough. It's rough in a lot of places, by the way."
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Although the breakthrough made at the summit marks just the start of a diplomatic process, it could bring lasting change to the security landscape of Northeast Asia, just as former US president Richard Nixon's visit to Beijing in 1972 led to the transformation of China.
Before the signing of what Mr Trump described as a "comprehensive letter", Mr Kim said the two leaders had a historic meeting and decided to leave the past behind. The world will see a major change, he said.
Mr Trump said he had formed a "very special bond" with Mr Kim and the relationship with North Korea would be very different.
"People are going to be very impressed and people are going to be very happy and we are going to take care of a very dangerous problem for the world."
Asked whether he would invite Mr Kim to the White House, Mr Trump said: "Absolutely, I will."
He called Mr Kim "very smart" and a "very worthy, very hard negotiator."
"I learned he's a very talented man. I also learned that he loves his country very much."
During a post-lunch stroll through the gardens of the Singapore hotel where the summit was held, Mr Trump said the summit had gone "better than anybody could have expected".
Mr Kim stood silently alongside, but the North Korean leader had earlier described their meeting as "a good prelude to peace".
Both men walked to Mr Trump's bullet-proof limousine, nicknamed "The Beast", and looked in at the rear seat, with Mr Trump apparently showing Mr Kim something inside. They then resumed their walk.
They had appeared cautious and serious when they first arrived for the summit at the Capella hotel on Singapore's Sentosa, a resort island with luxury hotels, a casino, manmade beaches and a Universal Studios theme park.
But, with cameras of the world's press trained on them, they displayed an initial atmosphere of bonhomie as they met on the veranda of the Capella, a refurbished 19th century British regimental officers' mess.
After a handshake, they were soon smiling and holding each other by the arm, before Mr Trump guided Mr Kim to the library where they held a meeting with only their interpreters.
Mr Trump had said on Saturday he would know within a minute of meeting Mr Kim whether he would reach a deal.
Inside, they sat alongside each other against a backdrop of North Korean and US flags, with Mr Kim beaming broadly as the US president gave him a thumbs up.
The combatants of the 1950-53 Korean War are technically still at war, as the conflict, in which millions of people died, was concluded only with a truce.
After initial exchanges lasting around 40 minutes, Mr Trump and Mr Kim emerged, walking side-by-side through the hotel before entering a meeting room, where they were joined by their most senior officials.
Mr Kim was heard telling Mr Trump through a translator: "I think the entire world is watching this moment. Many people in the world will think of this as a scene from a fantasy ... science fiction movie."
Asked by a reporter how the meeting was going, Mr Trump said:"Very good. Very, very good. Good relationship."
Mr Kim also sounded positive about the prospects of peace.
"We overcame all kinds of scepticism and speculations about this summit and I believe that this is good for the peace," he said.
"I believe this is a good prelude for peace."
Mr Trump was joined by Secretary of State Mike Pompeo, National Security Adviser John Bolton, and John Kelly, White House Chief of Staff, for the expanded talks, while Mr Kim's team included former military intelligence chief Kim Yong Chol, foreign minister Ri Yong Ho and Ri Su Yong, vice chairman of the ruling Workers' Party.
As the cameras captured the moment, Mr Trump quipped: "Very nice. Getting a good picture everyone, so we all look nice and handsome and thin ... perfect".
In the hours before the summit began, Mr Trump expressed optimism about prospects for the first-ever meeting of sitting US and North Korean leaders, while Mr Pompeo injected a note of caution whether Mr Kim would prove to be sincere about his willingness to denuclearise.
Mr Pompeo said the summit should set the framework for "the hard work that will follow", insisting that North Korea had to move toward complete, verifiable and irreversible denuclearisation.
North Korea, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Mr Kim's dynastic rule.
Sanctions on North Korea would remain in place until that happened, Mr Pompeo said yesterday. "If diplomacy does not move in the right direction ... those measures will increase."
The White House said later that discussions with North Korea had moved "more quickly than expected" and Mr Trump would leave Singapore today after the summit, rather than tomorrow, as scheduled earlier.