After three years of piecemeal crisis-fighting measures, agreeing on a banking union would lay a cornerstone of wider economic union and mark the first concerted attempt to integrate the bloc's response to problem lenders.
Finance ministers and officials from the bloc's 27 countries met in Brussels to attempt to advance talks on divisive questions such as the scope of the European Central Bank's cross-border supervisory powers, which would be a first step in a banking union.
At a news conference with Germany's Wolfgang Schäuble, French finance minister Pierre Moscovici said agreement could be reached soon.
"Work continues for a few more weeks to reach a definitive agreement, but France and Germany aim to reach the same objectives with the same calendar, the same method," he said.
Critical remarks from other countries painted a different picture.
Sweden flagged what it believes to be a fundamental flaw in the plan - that there is no acceptable way of allowing non-euro states to join the scheme on an equal footing with those using the currency. It raised the prospect of a laborious change to EU law to set up the system.
"The ECB could be the supervisor but then we need to consider a treaty change," Swedish Finance Minister Anders Borg told reporters. "Either you must change the treaty so it's clear that every member is treated equitably or you need to move it [supervision] outside of the ECB."
His concerns were echoed by Austria's finance minister, who said countries outside the euro that want to join the scheme needed to be put on a par with euro states. This will be difficult as bank supervision will be run by the ECB and it is answerable only to the 17 countries using the euro.
"Non-euro members also want to participate and want to have equal participation procedures," Maria Fekter told peers, in comments broadcast on television, adding: "It could also be a question if the treaty change would be the better solution."
Michel Barnier, the European Union official responsible for designing the new supervision law and negotiating its implementation, said although treaty changes were possible in the future they were not on the table now.
The European commissioner responsible for regulation also sought to play down talk of delay in reaching agreement on the framework beyond the year-end, a target suggested by EU leaders in June. "I think agreement in December is possible although it's difficult," he said.
There is growing concern in Brussels that the construct is already crumbling in the face of powerful opposition both within and outside the euro.
Germany, the leading economy in the eurozone, is pushing to restrict the ECB's oversight to top banks while Britain, the biggest country outside the euro, wants to stop the central bank from taking decisions that infringe on its interests.
"We don't want a banking supervisor that doesn't have any teeth," said one official. "It should not be a coordinating body. The final decision must be made by the ECB and that goes for small banks as well as systemic ones."
Making the ECB the supervisor for lenders chiefly in the 17 countries that use the euro would be the first of three pillars in a banking union and one EU leaders have committed to complete by the year-end.
When supervision is in place, it would pave the way for the eurozone's rescue fund, the European Stability Mechanism, to help troubled lenders directly rather than via their governments, breaking with the previous approach where smaller states such as Ireland were left to solve their banks' problems alone.
Longer-term plans for a central scheme to wind down banks and a combined means of deposit protection to prevent bank runs would complete the banking union, underpinning lenders and the euro currency.
Britain has proposed a means for countries outside the banking union to stop the ECB taking decisions that could affect their interests. Since Britain would dominate this group, many countries see this as London effectively demanding a veto and oppose it.
Germany, which wants to keep primary oversight of the country's community savings banks, wants to limit the ECB's remit to systemically important lenders.
It is also worried that the more banks are included in the scheme, the higher the potential cost when, as is ultimately planned, supervision is backed up by a central fund to pay for the closure of troubled lenders. Germany, Europe's largest economy, would have to foot a large part of any such bill.
The EU ministers also discussed new rules governing the amount of capital banks must set aside to cover unpaid loans and other risks as well as a proposal, backed by Germany but opposed by Britain, to cap bankers' bonuses at three times their salary.
Barnier urged EU countries to back stiffer rules on bonuses, after earlier late-night talks on Monday between country diplomats and the European Parliament failed to reach agreement.