Instead, the administration credited the release to its diplomatic intervention.
Asked whether the USA wanted to see an Iran-style global embargo to deny exports of petroleum and other products to North Korea, Mr Tillerson said that this would only work if Russian Federation and China co-operated.
Such direct consultations between the two governments are rare.
Trump called Rodman "smart" for his 2013 trip to North Korea, Politico reported at the time.
The US has in the past accused North Korea of detaining its citizens to use them as pawns in negotiations over its nuclear weapons programme.
But the fact that he had been kept, comatose, in North Korea for more than a year could worsen the already tense relationship between Pyongyang and Washington.
Mr. Rodman is a Hall of Fame professional basketball player who formed a personal relationship with the diminutive North Korean dictator Kim several years ago, traveling to North Korea to give basketball demonstrations.
Warmbier was a University of Virginia undergraduate when he chose to go to North Korea with a tour group.
He was sentenced in March 2016 to 15 years' imprisonment with hard labor and, according to his parents, fell into a coma shortly thereafter.
Richardson, a Democrat, credited the Department of State with securing Warmbier's return from North Korea without any preconditions but said a forceful response from the USA government would be required "if its determined that there was a cover-up and Otto's condition was not disclosed and he didn't get proper treatment". Otto Warmbier is reportedly still in a coma, according to the Associated Press, and he was transported to the University of Cincinnati Medical Center upon his arrival in the country. His parents say he's on a Medivac flight on his way home.
Rodman said the issue of several Americans detained by North Korea is "not my goal right now", in remarks made in Beijing before the release of Warmbier was publicly disclosed. Thousands of US troops are based in South Korea, and the Demilitarized Zone between the North and South is one of the most heavily fortified borders in the world. "Out of respect for the privacy of Mr. Warmbier and his family, we have no further comment on Mr. Warmbier".
Seoul said last month that it will flexibly resume civilian inter-Korean exchanges to an extent that the move does not compromise the global sanctions regime.
North Korean state-run media said early past year that Warmbier was arrested for what they described as "a hostile act" against the regime. "We'll be relieved to have him home and are looking forward to surrounding him with people who love him".
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A Wyoming man held prisoner in North Korea for over a year is returning to OH tonight, but the news isn't all happy. The official referred to them as "hostages".
Jeffrey Fowle, another US tourist from OH detained for six months at about the same time as Miller, was released just before that and sent home on a USA government plane. North Korea accuses Washington and South Korea of sending spies to overthrow its government.
The North Koreans later urgently requested another meeting in NY. Yun insisted on Warmbier's immediate release on humanitarian grounds, officials said, and the North Koreans agreed.
He informed Secretary of State Rex Tillerson, who consulted with Trump, the officials said. Yun and two physicians flew to Pyongyang and visited Warmbier on Monday. He was evacuated on Tuesday.
As the Americans continued to push to see all four, North Korea's ambassador to the United Nations urgently requested a meeting with Yun in NY, according to Trump administration officials, who spoke on condition of anonymity about the secret arrangements.
In the past, North Korea has held out until senior USA officials or statesmen came to personally bail out detainees.
Warmbier was flown out of North Korea on the same day that Dennis Rodman, the controversial former basketball star, arrived for his fifth visit to Pyongyang.
In the past, North Korea has held out until senior US officials or statesmen came to personally bail out detainees.
Previous detainees have been released after visits from high-profile Americans, including former presidents Jimmy Carter and Bill Clinton.
Richardson, a former Democratic congressman, U.N. Ambassador, U.S. energy secretary and ex-governor of New Mexico, welcomed Warmbier's release but said "we are deeply concerned regarding his health".
Phil Robertson, deputy Asia director at Human Rights Watch, said, "It's clear that Pyongyang has committed a grave injustice against Otto and his family, and the news that he may be returning with a serious medical problem raises concerns about what happened to him in North Korean custody". Representatives of PUST have stated that the arrests of Tony Kim and Kim Hak Song are "not connected in any way" with the university's work.
Together with Kenneth Bae, the DPRK government released Matthew Todd Miller, another US citizen who tore his visa upon arrival at Pyongyang International Airport in an alleged attempt to seek asylum and was later given a six-year sentence for similar charges. He had also taught at the university.