In 1982, Mørk became the first Scandinavian musician to reach the finals of the Tchaikovsky Competition in Moscow since Arto Noras in 1966, and won the sixth prize.

In 1994, he toured the United States with the Oslo Philharmonic, including debuts at Carnegie Hall and the Kennedy Center.

In April 2009, Mørk experienced an infection of the central nervous system, presumably caused by a tick bite he received in the United States in 2006, with subsequent encephalitis, and paralysis in the shoulder muscles of the left arm.

[4] After 18 months away from concert activity, during which time he was awarded the 2010 Sibelius Prize,[5] Mørk resumed his career.

For more than 30 years, he performed on a rare Domenico Montagnana cello (Venice, 1723), whose scroll was made by Stradivarius.