BBC News with Marion Marshall

European Union leaders are meeting in Brussels to

thrash out

the details of plans to fix the eurozone's sovereign debt crisis. A statement by the leaders after the first round of talks said agreement had been reached on strengthening banks or

recapitalisation

. Andrew Walker is in Brussels.

Tackling the weakness of the banks was the area where European countries had made most progress ahead of the summit. In a statement, the leaders said there's broad agreement that banks should meet higher standards of financial strength. The statement said what that standard would be, although it did not give a figure for how much extra the banks would have to raise. It said the banks should try to get the money privately but if necessary they would have to turn to public funds. The decision was taken by the full European Union. Leaders of the 17 countries that use the euro are continuing discussions separately on other measures to establish financial stability.

As he arrived for the meeting, the Greek Prime Minister George Papandreou said Greece was doing its best to improve its economy. But he said the talks in Brussels weren't simply about saving the single currency but about

safeguarding

the entire EU unity project.

"Now is the time for the European leadership collectively to take decisions to end the uncertainty, end the crisis, turn the page and make sure we make a big step forward for the better future and prosperity and security of our peoples in Europe."