EU paymaster Germany criticised the Greek proposal as "not a substantial solution" as it failed to fulfil bailout conditions.
Plans underway by Angela Merkel's Chancellory could see the power to deal with struggling banks move from national to European level.
Greece's international lenders have agreed to give the country two more years to make the cuts demanded of it.
Eurozone leaders have sealed a new bailout for Greece that will fix its immediate financing needs but is unlikely to revive its shattered economy.
Eurozone ministers have told Greece they could not go ahead with an agreed deal to restructure privately held debt until it guaranteed reforms.
EU leaders are working to bolster a bailout fund to help prevent contagion in bond markets, amid growing US pressure to staunch the debt crisis.
EU leaders are holding talks to try to hammer out a plan for tackling the eurozone debt crisis, but a breakthrough is not expected until Wednesday.
The world's leading economies are pressing Europe to act boldly within eight days to resolve the eurozone's sovereign debt crisis.
The world's leading economies kept the pressure on Europe to sort out its debt crisis, with the urgency to be expressed at the end of the meeting.
Greeks raged against a wave of austerity on Wednesday after finance ministers failed to agree how to make private creditors contribute to a bailout.