The state news agency claimed that the student entered North Korea nominally for tourism, though the real intention was to undermine North Korea's unity under the USA government's acquiescence and control.
Pyongyang's Korean Central News Agency identifies the student as Otto Frederick Warmbier.
He was in North Korea with Young Pioneer Tours, a China-based company founded in 2008.
UVA's student directory has an Otto Frederick Warmbier listed as an undergraduate commerce student.
"Despite what you may hear, North Korea is probably one of the safest places on Earth to visit", the company says on its website.
Johnson said Young Pioneer Tours was in touch with Warmbier's family and United States officials.
The U.S. Embassy in Seoul said it was aware of the report.
Tensions are now running high on the Korean peninsula, as North Korea braces for fresh sanctions in the wake of the fourth nuclear test it carried out January 6. Those arrested have sometimes read statements of guilt that they later said were coerced.
If confirmed, the student would be the third Western citizen held in North Korea. It said a man identified as Kim Dong Chul was being held by the North and said authorities had accused him of spying and stealing state secrets.
U.S. Rep. Brad Wenstrup, whose district includes the area where Warmbier went to high school, also tweeted Friday that his office was trying to contact the State Department "to assist however possible in getting Mr. Warmbier home".
In recent years, North Korea has taken a number of Americans into custody, often for activities related to spreading Christianity and often only releasing them when a high-profile dignitary visits Pyongyang.
State Department spokesman John Kirby, citing "privacy considerations", declined to comment beyond acknowledging the reports of Warmbier's arrest and stressing that the welfare of U.S. citizens was always a top priority. Critics say such trips have provided diplomatic credibility to the North. In 2014, North Korea called for a high-level US delegation to come and discuss the release of two Americans then under detention.
North Korea is holding at least three South Koreans and one Canadian.
South Korean-born Canadian pastor Hyeon Soo Lim was sentenced last month to hard labour for life, according to state media.
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However, Tuesday's announcement by the Supreme Court gave them and around 20,000 other similar families in the Upstate hope. The court in 2012 and 2015 rejected conservative challenges to his signature healthcare law.
