However, they gave few details of the new proposals, which the current Greek EU presidency will take into more talks Wednesday with Parliament and the European Commission, the EU's executive arm.
"We defined, in an intensive debate, on which points the presidency can move towards the Parliament," German Finance Minister Wolfgang Schaeuble said.
"It is clear that we cannot accept on all points the wishes of the Parliament but we are clearly ready to find solutions," Schaeuble said as the meeting closed.
There are two main sticking points for MEPs, whose approval is required before the bloc's developing 'banking union' can come into force.
First is who will decide and how to close a failing bank.
The second is the legal status and 10-year phasing in period of a 'resolution' fund which will cover the costs.
After months of difficult negotiations, EU leaders agreed in December what is known as the Single Resolution Mechanism, designed to close failing banks in a safe and orderly fashion and so avoid a repeat of the debt crisis crash.
This SRM will work alongside a new regulator, run by the European Central Bank, which will supervise the eurozone's 130 biggest lenders from November.
Closing down a bank is a costly and politically charged step and so EU leaders agreed a decision-making structure which gave them the final say and minimised the role of the European Commission.
Parliament objected strongly to this proposal and warned again last week it could not accept a formula which allows "political power games" when closing a bank requires speed and effectiveness.
Parliament also believes the plans for the accompanying fund, paid for by the banking industry, is too unwieldy and its phasing-in period too long.
The fund is also to be set up under a treaty between member states, not under EU rules, effectively excluding Parliament from the process.
A recent vote in Parliament damned the proposals as an "overly complex and politicised decision-making process for winding up banks."
Greek Finance Minister Yannis Stournaras told a closing news conference he could now go into Wednesday's talks with "extra flexibility" on the key points.
"This is a very difficult issue," Stournaras said, declining to give precise details of what leeway ministers had agreed to give him.
"In certain of the ... elements we were more forthcoming, in some elements, less forthcoming," he said, adding: "I think we have moved foreward on some of Parliament's (concerns)."
Pressed on the changes, Stournaras said the meeting had discussed "certain ideas for speeding up ... the intention is for the process of resolution to be more rapid in the decision-making."
Ministers going into the talks had voiced cautious optimism that some progress was being made and all stressed the need to get an agreement as soon as possible ahead of elections for Parliament in May.
If that timetable is not kept, the plans may hang fire until the end of the year until a new EU leadership is named and is ready to take up the issue again.
Banking union is seen as essential to stabilise the financial system and buttress the single euro currency bloc whose failing banks nearly wrecked the whole project at the height of the debt crisis.
"It is now time to conclude the talks," French Finance Minister Pierre Moscovici said as he arrived for the discussions.
"There are only a few things left to do but they are very technical," Moscovici said, adding: "It is essential in my view to stick to the timetable."