Two of the men, agricultural expert Kim Hak-song and former professor Tony Kim were arrested in 2017, while Kim Dong-chul, a South Korea-born American businessman and pastor in his 60s, was sentenced to 10 years' hard labor in 2016.
He underscored that he was looking forward to meeting with North Korean Leader Kim Jong-un, adding that the venue and place were finalised.
The commentary went on to call "foolish" the idea that "support by Trump and neighboring countries" helped make the summit successful.
"For decades, we have been adversaries".
In a statement, White House Press Secretary Sarah Huckabee Sanders said: "President Trump appreciates leader Kim Jong Un's action to release these American citizens, and views this as a positive gesture of goodwill".
"This is not a result of sanctions that have been imposed from outside", he said. Trump has said that his pressure tactics have brought North Korea to the negotiating table.
The release of American student Otto Warmbier a year ago was secured after Joseph Yun, the State Department's then-special representative for North Korea policy, made a secret trip to Pyongyang.
Hours before Pompeo landed, Trump yanked the United States from a nuclear deal with Iran, complicating the prospects of persuading Pyongyang to surrender its atomic arsenal.
Both worked at the Pyongyang University of Science and Technology, which bills itself as the only privately run university in the North Korean capital.
Trump has demanded that North Korea give up its nukes, while Kim has offered few indications about what he is willing to concede or what he will demand in return.
During his brief visit, Pompeo said the U.S.is committed to working with North Korea to establish peace on the Korean peninsula. The president said Pompeo has worked out the place and time of the summit, in talks with North Korean officials.More news: Luke Cage Gets Knocked The F*ck Out In New Season 2 Trailer
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The upcoming U.S. -North Korea summit has sparked a flurry of diplomacy, with Japan, South Korea and China holding a high-level meeting in Tokyo on Wednesday.
"We think relationships are building with North Korea", Trump said in a televised address from the White House.
Pompeo's first trip to Pyongyang, over Easter weekend before he was confirmed as secretary of state, was a closely held secret.
Pompeo took office just two weeks ago, but the West Point grad is a former director of the Central Intelligence Agency.
USA officials were infuriated by Warmbier's death and Trump has accused North Korea of brutally abusing the American student.
Trump didn't disclose the date and location of his planned summit with Kim, but the release of the American detainees was heralded as a significant diplomatic signal by Pyongyang.
Nauert said Pompeo also secured the release of three USA citizens and is delighted to bring them home.
A North Korean official came to the hotel shortly afterwards to inform Pompeo that Kim had granted their release, according to a senior United States official present for the exchange. Credit to anyone but North and South Korea for the event occurring is "seriously contrary to the principle of national independence", the piece argues.
In past weeks, Trump had talked up the demilitarized zone between North and South Korea as a potential site for the Kim meeting, saying it was intrigued him to negotiate at the site of the nuclear dispute.
China's official Xinhua news agency cited Kim as telling Xi there was no need for North Korea to be a nuclear state "as long as relevant parties abolish their hostile policies and remove security threats against" the country. He added that a political resolution of tensions on the Korean Peninsula and denuclearization should proceed in stages, with all sides moving in concert.
Talk of the captives' release had increased as the US and North Korea's regime engaged in rare talks - and worked to arrange a meeting between Trump and Kim Jong Un.
"We will not relieve sanctions until such time as we have achieved our objectives", Pompeo said.
The upbeat announcements on the North Korea front came just hours after it was revealed that Trump's personal lawyer Michael Cohen received, into a business account he controlled, $ 500,000 from a Russian oligarch with close ties to Vladimir Putin.