Mr Trump said that a "lot of bad things happened" to Mr Warmbier, but added: "At least we got him home to be with his parents, where they were so happy to see him, even though he was in a very tough condition".
Other high-profile tour operators who take travelers to North Korea also said this week that they are "reviewing" their policies regarding traveling Americans in the wake of Warmbier's death, The Associated Press reported.
The China-based travel agency that organized a trip to North Korea for an American college student who died after being released in a coma from North Korean detention said it would no longer take USA citizens to the country.
Warmbier's parents haven't cited a cause of death, but "awful, torturous mistreatment" by North Korea.
The funeral for Warmbier will be held at 9 a.m. Thursday at Wyoming High School, where he was an athlete and salutatorian of his 2013 class.
Mr Warmbier had suffered severe brain damage, and was medically evacuated from North Korea on 13 June to a hospital in his home city of Cincinnati, Ohio. "The results would have been a lot different".
If the North Koreans were smart they would release them all to atone for what they did with Otto [Warmbier], as a sign of contrition, a human rights gesture.
His death led to strong condemnations of the regime and speculation about the implications.
ADDING MULTIMEDIA AirAsia World Champions for Ninth Time at Skytrax
In addition, Azul was also named for the second consecutive year as the victor of the Best Airline Staff in South America award. Last year, Emirates , a regional rival, stole the show.
Otto's father blasted Obama during a news conference at the tie of his son's release, when cued up with a question as to what more could have been done to secure Otto's release before Trump entered the White House.
The Warmbier family confirmed on Monday that he had died.
"If China is not going to solve North Korea, we will", Trump told the Financial Times in April.
While Beijing may attempt to use such leverage to free Americans in the North, its influence is limited, said Jin Qianyi, a professor at Yanbian University's Institute of Northeast Asia Studies, which sits along the border with North Korea. He was sentenced in March 2016 to 15 years in prison with hard labour.
There was no immediate word from the family about why relatives declined an autopsy, which may have shed more light on the cause of the neurological injuries that left him in a coma.
Sen. Rob Portman of OH also had tough words for North Korea.
But around the time Spicer said that, Trump tweeted he appreciated China's efforts but "it has not worked out". "It puts us in a really precarious situation when Americans are detained there".
Chinese Foreign Ministry spokesman Geng Shuang called Warmbier's death a "tragedy".
Three other Americans are still imprisoned in North Korea, accused of crimes against the Pyongyang regime.
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