While he was moved to a midfielder position at Köln, Olsen continued to play as a libero for Denmark. He captained Denmark at the 1988 European Championship, which ended in the preliminary group stage. During the tournament, Olsen proved too slow for the libero position, and was moved up as defensive midfielder, leaving the libero position for Lars Olsen. Morten Olsen ended his international career following the 1988 European Championship, having played 99 national team games, but was called up again 10 months later. Olsen became the first Dane to play 100 games for the national team in April 1989, before ending his national team career in June 1989. Olsen played a record 102 games and scored four goals for the national team, and set a record of 50 games as Danish national team captain. His team captain record was broken by Lars Olsen in 1992, while his game tally was bested by Peter Schmeichel in 1998. In his entire international career, Morten Olsen only got one yellow card.