BERLIN (Reuters) - Hungarian Prime Minister Viktor Orban has said he is worried about a loss of confidence in the European project, arguing that contempt for European Union rules has put the single currency and internal market at risk.

A staunch critic of the EU, the Hungarian leader was quick to warn after Britain's vote last month to leave the bloc that the EU will face more big challenges if it fails to get to grips with the migration crisis.

"The main reason for the crisis (in Europe) and uncertainty is that through the disregard for rules the two biggest European achievements are at risk: the common currency and the internal market secured by Schengen," Orban wrote in an opinion piece for Germany's Frankfurter Allgemeine Zeitung.

He was confident Britain would carve out its future after its June 23 referendum vote to leave the EU.

"I'm not worried about the Brits, as we are talking about the most experienced democracy in Europe ... Let's rather worry about ourselves," wrote Orban.

Lamenting what he said were doubts among a growing number of EU citizens about the project, Orban said the bloc needed to do more to engage people in tackling crises.

"We need every person, every nation, every member country. Institutions can't make up for that. They need to help and coordinate, but not push the member states into the background," he said in an apparent dig at the European Commission.

(Writing by Paul Carrel; Editing by Catherine Evans)