Warmbier was jailed in North Korea in 2015 during an organised tour and died after being returned to the US in a coma after 17 months in detention.
Earlier reports said that the US had been billed $2m (£1.5m) for the student’s medical care.
North Korea had allegedly demanded the bill be paid before he was allowed to return home.
Mr Trump denied the claim on Twitter on Friday. He wrote: “No money was paid to North Korea for Otto Warmbier, not two Million Dollars, not anything else.”
Public Comment of what Trump said
“That better turn out to be true. I wish he had paid ransom for that young man, but having said this, it better be true. “
” Whether the funds were ever transferred, he PROMISED he would. “
“The Donald… A National Embarrassment…! “
Why would anyone believe anything he says?
” So Trump is saying that he treated North Korea like a business partner, and stiffed them. “