Spain came from a goal down to draw with Italy in their Group C opener but were criticised for not starting with a striker as Italy's five-man midfield stifled their creativity.
Confident predictions that Spain could become the first team to win three successive major international titles have quietened since, but Mourinho still believes in them.
"Spain is the world champion and no doubts about that," Mourinho told reporters in Singapore on Thursday.
"They are one of the best teams in the Euros, so normally, if things go in the right direction, Spain has to qualify and Spain has to go through and Spain has to compete maybe with Germany and maybe a couple of other teams to be champion of Europe."
The Portuguese did not hold such confidence in his compatriots, who bounced back from an opening loss to Germany to beat Denmark 3-2 on Wednesday.
However, the unpredictability of the 16-team tournament gave him hope Portugal could spring a surprise and win the tournament for the first time.
"Now they don't depend on other teams they depend only on themselves so if they can do a job against Netherlands, Portugal is in the quarter-finals," Mourinho said.
"I don't think Portugal is one of the two, three best teams in the competition, but these short competitions with knockout in 90 minutes and sometimes extra time and penalties so if Portugal reach the quarter-final anything can happen."
