The North had earlier Friday denied torturing or mistreating Warmbier, in the first official reaction to his death.
Warmbier's parents said the North Koreans claimed their son had contracted botulism before taking a sleeping pill, which led him to slip into a coma.
The agency said: "Our related institutions are treating criminals who committed crimes against (our) republic strictly based on domestic law and worldwide standards, and Warmbier was no different", the KCNA said.
The 22-year-old died in an OH hospital on Monday after North Korea released him for what they described as humanitarian reasons.
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Mr Warmbier was released earlier this month and returned to the US, where he was described as being in a "state of unresponsive wakefulness". He was released a week later. President Trump condemned the North's "brutality", and other political leaders demanded that it explain what happened to Mr. Warmbier. As the rogue regime repeatedly threatened the USA and its regional allies, testing missiles at least nine times since Trump's election, the administration looked to China to help.
Warmbier was laid to rest in Wyoming, Ohio, on Thursday.
His family and others have blamed North Korea for his condition.
Rodman's agent, Chris Volo, says his client personally lobbied the Pyongyang government for Warmbier's return home. "But I want these two sides to get together and try to figure something out". The Obama administration, the spokesman said, never asked for his release. "We don't believe anything they say". No one knew that. We jumped up and down ...
DPRK is short for the North's official name, the Democratic People's Republic of Korea.
His former soccer coach, Steve Thomas, said Warmbier came from a religious family and was involved in mission trips and a birthright trip to Israel. The adventures include booze cruises down a North Korean River and bar crawls in Pyongyang.