US Secretary of State Mike Pompeo says that the Trump administration would like to see “major” North Korean nuclear disarmament in the next two and a half years, following the historic meeting between President Donald Trump and North Korean leader Kim Jong-un in Singapore.

Mr Pompeo made the statement during a trip to South Korea, saying that the US goal is to see major headway by the end of Mr Trump’s first term.

The US secretary of state was visiting Seoul to brief South Korean leaders on the negotiations between the US and North Korea that had occurred in Singapore.

“I am ... confident that there will be in-depth verification,” Mr Pompeo said of how any denuclearisation effort would be monitored, adding that the initial document signed by the two leaders at the summit had not encompassed the entire range of discussions held behind the scenes.

“Not all of that work appeared in the final document. But lots of other places where there were understandings reached, we couldn’t reduce them to writing, so that means there’s still some work to do, but there was a great deal of work done that is beyond what was seen in the final document that will be the place that we will begin when we return to our conversations,” Mr Pompeo, who had flown to Seoul from Singapore, told a group of reporters.

While Mr Trump hailed the negotiations with North Korea as a strategic success of historic proportions, saying that there was “no longer a nuclear threat from North Korea”, critics said that the joint statement between the US and North Korea at the end of the Singapore summit was short on details, and that Mr Trump appeared to offer too many concessions compared to the commitments that North Korea put on paper.

Singapore Summit: historic first meeting between Trump and Kim Jong-un Show all 20 1 /20 Singapore Summit: historic first meeting between Trump and Kim Jong-un Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim leave following their historic meeting AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim sign a document committing to peace between their nations, amongst other things EPA Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump holds up a document that both he and Mr Kim have signed AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un The two leaders reach out to shake hands for the first time AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim shake hands as they meet for the first time Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim walk off stage, following their historic meeting Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim take a stroll after their meeting on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim interrupt their stroll to talk to the media AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Kim and Mr Trump look out over a balcony at the Capella hotel, where they held their meeting on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump takes questions at the press conference following his meeting with with Mr Kim AP Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump appreciates the crowd in the press conference following his meeting with Mr Kim Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump travels to the Istana ahead of the summit with Kim Jong Un on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Kim Jong Un travels to the Istana ahead of the summit with President Trump on June 12 Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Kim poses for a photo with Singapore's Finance Minister Vivian Balkrishnan and Education Minister Ong Ye Kung ahead of the summit with Mr Trump Twitter/Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump shakes hands with Singapore Prime Minister Lee Hsien Loong, meeting on Monday June 11 in the Istana, Singapore's presidential palace AP Singapore Summit: historic first meeting between Trump and Kim Jong-un At a working lunch on Monday, Singapore's Prime Minister surprised Mr Trump with a birthday cake, in early celebration of his 72nd birthday later in the week EPA Singapore Summit: historic first meeting between Trump and Kim Jong-un US Secretary of State Mike Pompeo answers questions about the summit at a press briefing in Singapore on Monday, June 11 Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un US President Donald Trump arrives at the Paya Lebar Air Base in Singapore on June 10, two days prior to his summit with North Korean leader Kim Jong Un Reuters Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump and Mr Kim met on Tuesday June 12 in the Capella hotel on the island resort of Sentosa, just off the south coast of Singapore AFP/Getty Singapore Summit: historic first meeting between Trump and Kim Jong-un Mr Trump boards Air Force One following the summit AFP/Getty

Among those concessions was a promise to suspend joint military exercises between the US and South Korea on the Korean peninsula, which Mr Trump has criticised as being too costly and “provocative”. Mr Pompeo said Mr Trump would resume military exercises with South Korea if North stops negotiating in good faith.

The secretary of state indicated that he is not sure yet when the US and North Korea might reassume negotiations over the country’s nuclear programme, but indicated that talks were likely to begin again in short order.

“I don’t know exactly what the timing will be for our next conversation with the North Koreans. I would anticipate it will be fairly quickly after we return to our home countries,” Mr Pompeo said.

“I don’t know exactly what form that will take, but I’m very confident that by some time in the next week or so we will begin the engagement,” Mr Pompeo said.

Pyongyang state media, the Korean Central News Agency (KNCA), said Mr Trump had expressed his intention to offer security guarantees to North Korea and lift sanctions “over a period of good-will dialogue” between the two countries. It said Mr Kim had said the North could take unspecified “additional good-will measures of next stage commensurate with them” if the US takes genuine measures to build trust.

The North Korean report quoted Mr Trump as crediting Mr Kim’s “proactive peace-loving measures” for having created the atmosphere of peace this year. It also suggested Mr Trump had adopted North Korea’s preferred phased approach towards any denuclearisation process, saying the two men had agreed to the “principle of step-by-step and simultaneous action”.

Mr Trump, upon landing back in Washington on Wednesday morning, said that his summit with Mr Kim makes the world safer.

“Just landed – a long trip, but everybody can now feel much safer than the day I took office. There is no longer a Nuclear Threat from North Korea. Meeting with Kim Jong Un was an interesting and very positive experience. North Korea has great potential for the future!” Mr Trump wrote on Twitter in between congratulatory notes to Republicans who had won their primary races the night before, and just an hour after an attack on Robert De Niro, whom he claimed has a low IQ.

But critics of the president, including Senate Minority Leader Chuck Schumer, said that they see the Singapore meeting as little more than a photo opportunity for Mr Trump and Mr Kim.

“The emphasis on showmanship as opposed to substance at the #NorthKoreaSummit will not serve America or the prospects for peace well in the long run,” Mr Schumer wrote on Twitter.