Spanish Finance Minister Elena Salgado - whose country now holds the EU presidency - said she is "not worried" that Greece will default, but refused to discuss the possibility of a bailout.
"I think Greece is going to do all that is necessary to avoid that," she said before chairing an EU finance ministers meeting.
Salgado waved aside talk of an alternate plan in case Greece fails to make good on its debts - obligations that have sharply raised its borrowing costs because of fears the country may default or seek a bailout.
A bailout would be a first for the decade-old eurozone, which now looks vulnerable and faces painful, unpopular measures such as budget cutbacks and higher taxes.
After a meeting Monday of the 16 eurozone finance ministers, Luxembourg premier Jean-Claude Juncker - the group's chairman - announced an overhaul of how euro nations coordinate their economies. He called for countries to be formally warned if they are running much higher inflation or average wages than their neighbors.
The Greek government has drafted an austerity program of deep spending cuts and tax hikes to assure financial markets - and Athens' EU partners - that it will reduce debt. The EU finance ministers are to debate the Greek measures in detail in February but the issue loomed large over Tuesday's meeting.
The European Union's economy commissioner, Joaquin Almunia, said the European Commission planned to carefully monitor how Greece is implementing the debt reduction measures, and that EU officials would check the government's policies at three stages, starting in June.
He also said the EU executive would seek the power to audit Greece's statistics, following a damning EU report last week that said Greece falsified economic data to make its budget deficit look smaller last spring and that statistics collection may be open to political influence.
Greece's problems show the flaws in the loose way that the eurozone countries handle their economies. They are supposed to stick to strict limits on deficit and debt - but have rarely done so, allowing their economies to diverge.
Juncker said finance ministers need to wade into wider issues on how the economy is run, urging them to influence their own government's policies on structural reforms - such as making the labor market more flexible.
From next month, they would be warned by the European Commission if their countries differ too much from the rest of the eurozone on broad policy guidelines or on specific areas such as inflation, wages or current account deficit. That warning would not be backed by any penalty.
"We need to broaden surveillance in the euro area," Juncker said, adding that closer monitoring should also extend to European countries whose currencies are linked to the euro and who hope to join the currency zone, such as Estonia and Latvia.
Despite market worries over other debt-laden eurozone countries, such as Ireland, Juncker said he didn't "see another country entering into a situation similar to that of Greece."
He set out plans for tighter management of the eurozone, saying the countries should hold an informal summit, publish statements after their talks and seek advice from think tanks.
A closer eye on the economy will be crucial as governments start withdrawing stimulus programs that have largely driven growth over the last two years.
