The negation talks that began Saturday early hours in Luxembourg ended in controversy in the euro zone and non-euro member states on the day.
They discussed how to form a system in which taxpayers' money would be used in the future as little as possible to rescue banks.
The ministers, however, are divided on, among other things, how the rules should be flexible to do.
Certain non-euro member states and France are in favor of a more flexible system, while Germany calls for stricter rules.
Despite their differences, the ministers, however, were optimistic about a positive outcome of the talks.
Ministers of Finance will continue negotiations till Wednesday. The goal is to get ready before the start of the EU summit on Thursday.
The system is seen as a step towards a common EU banking union.
