By Jan Strupczewski and Francesco Guarascio

BRATISLAVA (Reuters) - European Union finance ministers and central bank governors discussed on Friday the idea of a euro zone budget, called a "fiscal capacity", amid some scepticism if it was needed and under what conditions.

There was no agreement on any aspects of the idea, except that talks should continue.

"The majority agreed on the fact it is important to discuss these issues, and agreed it is not for tomorrow or the day after tomorrow. It takes some time," Slovak deputy finance minister Ivan Lesay told a news conference.

The idea of a euro zone budget has been around since the sovereign debt crisis in 2012 and is part of plans for further euro zone economic integration over the medium to long term.

It is seen as a necessary final stage of building a monetary union to provide a counterbalance, together with a euro zone treasury, to the monetary policy of the European Central Bank and as a way to help the single currency area absorb external economic and financial shocks.

But the issue is sensitive because it carries a risk that more fiscally prudent countries may end up bank-rolling spendthrift ones.

"There were very different opinions," Swedish Finance Minister Magdalena Andersson said on leaving the informal talks.

"Some countries are very enthusiastic whereas other countries were a lot less enthusiastic. So there is absolutely no agreement there should be a European fiscal capacity. We are not even close to talking about a timeline," she said.

Slovakia, which holds the rotating presidency of the European Union, outlined several options for the set-up of such a "fiscal capacity", also called "stabilization function" in a paper prepared for the ministers.

"Some ministers seemed to be in favor of a stabilization mechanism built around an unemployment scheme, others looked more towards investment-based mechanisms," European Commission Vice-President Valdis Dombrovskis told reporters.

"But there were also some doubts expressed by some other ministers that this may not be the time to launch new initiatives," he said.

Officials said there was agreement among the ministers and central bankers that before a euro zone budget could be constructed, euro zone countries would have to act to restore mutual trust between themselves through respect to already existing rules on budget deficit and public debt.

"There was a common view in the meeting that any additional initiative requires mutual trust among the countries that rules will be respected," said ECB Vice-President Vitor Constancio.

The Slovak paper prepared for the discussions noted that a euro zone budget could improve compliance with EU fiscal rules, now often disregarded and not enforced, because the money could be made available only to countries that obey the rules.

The fund could take the form of a European Unemployment Insurance Scheme, the paper said, complementing national unemployment plans. Under the scheme, countries that accumulate surpluses in economic good times could spend the money to help cover deficits in countries in recession.

Another option would be an investment fund that would finance large, pan-European infrastructure projects, similar to the European Fund for Strategic Investment now in operation, the paper said.

(Additional reporting by Jason Hovet, Tatiana Jancarikova and Shadia Nasralla in Bratislava)