Luxembourg's finance minister said Monday that if Greece cannot implement its reform promises, the eurozone group will have to go on without the country.

"I still think we should do our best to keep the eurozone with all of its members," Luc Frieden said at a conference in Washington.

"Our preferred scenario is Greece complying, the eurozone giving additional funds -- and I cannot insist enough on this aspect -- clear monitoring of the implementation of what Greece has promised to do," he said.

"If they don't do all this, I think then we must go on with 16 countries."

Frieden was speaking a day after Greece's political leadership committed to a tough austerity-and-reform package demanded by the European Union and private creditors in order to obtain a sweeping debt restructuring and new bailout program.

EU finance ministers are expected to meet Wednesday to decide whether Athens had done enough to merit a new 130-billion-euro ($170 billion) bailout.

But Frieden warned Greece had to follow through.

"If the Greek people, or the Greek political elite fails to apply all these conditions, and I do know that these are difficult times for the Greek people... I think they exclude themselves from the eurozone," he said.