The statement came despite the lack of concrete proof that North Korea will discontinue its nuclear program.
Pompeo dismissed a report by North Korean state media that indicated the USA would grant concessions to Pyongyang for gradual progress.
Mr Trump tweeted: "Just landed - a long trip, but everybody can now feel much safer than the day I took office".
Video footage aired Thursday by North Korean state media showing President Trump returning the salute of a North Korean military general in Singapore has drawn criticism from USA media. It seemed like the message from the Trump administration had been, you know, the trade in North Korea are linked.
But, Pompeo said that was not the case.
US Secretary of State Mike Pompeo has said there will be no sanctions relief for North Korea until it denuclearises. "Only then, there will be a relief from the sanctions".
Axios reported Thursday that the Israeli report makes a point of noting that a brief document signed by Trump and Kim fails to commit the North to "full, verifiable, irreversible denuclearization", which has always been Washington's position.
While acknowledging that there may be "very conflicting views regarding the outcome of the summit", the United States had been able to spare "the whole world. the fear of war - a nuclear war - as well as the long-range missiles", he said.
Replying on Twitter, the top Democrat on the House Intelligence Committee, Adam Schiff, said "North Korea is a real and present threat".
Mr Pompeo was speaking at a press conference in Seoul with his South Korean and Japanese counterparts.
5 latest North Korea summit developments: What you missed overnight
Kim Jong Un met Singapore Prime Minister Lee Hsien Loong shortly after his arrival, driving from the St. The US president had told reporters in Canada that he "felt confident" about Tuesday's talks with Kim.
Later, Pompeo traveled to Beijing were he spoke to China's foreign minister Wang Yi.
Putin added that Russian Federation is ready to "make all necessary efforts to establish ties, including in economic cooperation" with North Korea. Meeting briefly with Mr Pompeo on Thursday morning, Mr Moon said he was eager to hear how the United States and North Korea could "fully and expeditiously implement this great agreement".
Pompeo told Xi and other Chinese leaders during a meeting in Beijing that Washington "wants a lasting and stable peace regime" in the region, the department said.
Pompeo travelled from Singapore to South Korea to brief the US's regional allies on the summit, and on Trump's surprise announcement that he was ending routine US-South Korea military drills.
However, KCTV did capture one moment (which takes place at 22:35 in the video) that was largely missed by American audiences.
Trump could, but should not, relax sanctions against Pyongyang at any time, according to Democratic Senator Ben Cardin.
SHI YINHONG: (Through interpreter) If tomorrow Trump announces imposing tariffs on $50 billion worth of Chinese goods, China's promises to increase USA exports and make it easier for US companies to enter the Chinese market won't happen.
US officials said it was unclear what type of training involving USA and South Korean troops might now be stopped because of Trump's order to end the "war games", but the massive annual exercises that bring in nuclear-capable ships and warplanes from Guam and other USA bases in the region will likely end. Conservatives said the move displayed weakness from the USA on the world stage. She said details of military planning were not discussed.
This year marks the 70th anniversary of the establishment of diplomatic ties between Russian Federation and North Korea. All of these North Korean "Supreme Leaders" have a personality cult surrounding them.
In the military, returning a salute from a military officer of a friendly foreign nation is common practice for USA military officers and considered a display of military professionalism.
"My understanding is that Trump said that to enhance a momentum of dialogue between South Korea and North Korea", Kang said told reporters.