COPENHAGEN, Dec 12 (Reuters) - Denmark's Morten Olsen, one of the longest-serving national team coaches in world football, has had his contract extended by the Danish FA after a six month search for an alternative.

"The new contract covers the period from the end of the existing contract next summer to the finals of the European Championships in France in the summer of 2016," the FA said in a statement on Thursday.

Olsen's reign had looked to be over when Denmark missed out on next year's World Cup finals in Brazil after coming second to Italy in group B, with a tally of 16 points not good enough for a place in the playoffs.

The FA spent six months searching and consulting with experts in Denmark and internationally before deciding to extend the existing deal.

"I'm very proud of the trust my employer has shown in me, and that is a key support in my decision to accept a new period," Olsen was quoted as saying in the statement. (Reporting by Philip O'Connor in Stockholm, editing by Alan Baldwin)