However, the reports about Kim's health are disputed as North Korea has not made any official statement regarding it
The leaders met days after Trump abruptly cancelled the summit with the North Korean leader on June 12 and blamed Pyongyang's 'tremendous anger' and 'open hostility'.
North Korea last week warned that it may cancel the June 12 summit in Singapore between Kim and Trump if the US insists on it giving up nuclear weapons unilaterally.
Pompeo made the comments after attending a White House meeting between President Donald Trump and the visiting South Korean President Moon Jae-in.
US media said Trump scored a diplomatic victory with North Korea releasing the three imprisoned American citizens.
The White House statement comes a day after North Korea released three Americans who were detained in the country for months.
Trump's latest remarks appeared to be a pivot away from his often-bellicose rhetoric on North Korea and Kim, but Haley said there was "no turnaround" in the US stance.
The North has rattled the international community with a flurry of missile launches and its largest ever nuclear test in recent months in its bid to develop a warhead capable of striking the US.
North Korean leader Kim Jong-Un declared his country had achieved its long-cherished goal of full-fledged nuclear statehood after successfully testing ballistic missile.
The missile was fired into the Sea of Japan and flew for more than 900 km and reached a height of 4,000 km, which is the highest a North Korean missile has flown to date.
US President Donald Trump unleashed a twitter storm slamming "haters and fools" playing politics with US-Russia ties and declaring that he would never describe Kim Jong-Un as "short and fat".
Trump has embarked on a tour of Asia this week trying to rally regional support for curbing North Korea's nuclear weapons programme, warning that time is running out over the crisis.
US President Donald Trump on Wednesday offered North Korean leader Kim Jong-Un what he called "a path towards a much better future" as tensions soar over Pyongyang's nuclear ambitions.
South Korea is rolling out the red carpet for Trump as it seeks messages of assurance about the alliance and US resolve.
US President Donald Trump would "certainly be open" to meeting with North Korean leader Kim Jong-Un, he said in an interview broadcast today as he began an extended Asian tour.