He insisted that Trump had been explicit about the sequencing from the start. "I'm not going to give any insight into where we are in private talks", he said. "Only then will there be relief from the sanctions".
In remarks at a news conference in Seoul, the top USA diplomat added that any sanctions relief North Korea receives from the US will be linked to efforts to denuclearize.
The drill is designed in the spirit of the US-South Korean mutual defense treaty of 1953, the Pentagon said. "Maybe in a year you'll be interviewing and I'll say I made a mistake".
On the issue the world has been most fixated on - North Korea's pursuit of a nuclear arsenal meant to target the entire US mainland - Trump and Kim signed a joint statement that contained a repeat of past vows to work toward a denuclearized Korean Peninsula.
But the details of what is sure to be a complex and contentious process have yet to be settled.
Most experts assess that the North Korean leader got the better deal at the summit. "I feel it's good". But it "all depends on whether North Korea is serious about denuclearization".
"It's freakish but it might be that Kim Jong-un's interests and Donald Trump's interests align". He said negotiations would recommence "in the next week or so".
"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".
In the poll, Trump received a 51 percent approval rating for his handling of North Korea and also led the list of leaders who should take the most credit for the summit and the joint pledge. A Democratic senator from Connecticut, Chris Murphy, said of the outcome of the Singapore summit: "Kim's gulags, public executions, planned starvation, are legitimized on the world stage..."
Because of the summit, South Koreans, whose attitude toward the North Korean dictator has changed dramatically, would be in no mood to risk pyrotechnics launched by Washington against a North which no longer looked so threatening.
Pompeo was scheduled to travel next to Beijing before returning to Washington.
In the summit statement, Kim pledged to "work toward the complete denuclearization of the Korean Peninsula" - a stock phrase favored by Pyongyang that stopped short of longstanding United States demands for North Korea to give up its atomic arsenal in a "verifiable" and "irreversible" way.
Amid the many unknowns and unknowables of the Trump-Kim Singapore agreement one thing is certain: it represents a strengthening of China's position in north-east Asia.
Trump on President Xi of China: "He's an incredible guy". And how for the president to explain to the American people that aggressive war must be launched against someone he not long before embraced?
The lack of a definitive timeframe or verification mechanism for North Korea's nuclear disarmament prompted some former U.S. diplomats to question the utility of the summit and suggested Trump's tactics could undermine Washington's alliances with Seoul and Japan.
He said Pyongyang was committed to giving up its nuclear programme.
The exact terms of that agreement remain unclear.
Joseph Essertier: I think it's good to see there's a dialogue going on now between the governments of the USA and North Korea but unfortunately there is still little dialogue on a grassroots level between Americans and North Koreans because the country is in a state of war and has been continuously since the 1930's. No longer - sleep well tonight!'
Actually, concerns about North Korean missiles and nuclear weapons reached a peak last year, during Trump's first year in office, as the North conducted more tests and Trump and Kim aimed ever more fiery rhetoric at each other. "You can do anything", Trump said in the infamous tape.
"We save a fortune by not doing war games", Trump tweeted Wednesday, "as long as we are negotiating in good faith - which both sides are!"
Mr Pompeo was speaking at a press conference in Seoul with his South Korean and Japanese counterparts. Trump cast the decision as a cost-saving measure, but also called the exercises "inappropriate" while talks continue.
The tweet followed a New York Times story on the Trump administration's lack of scientific expertise, the president's questioning of the honesty of the American media at an global summit in Canada and his dismissal of diplomatic expertise in favor of using a "touch" and "feel" approach in his talks with Kim.