The French, the Italians and the Spanish are already backers of a banking union.
Yet, for some in the euro zone, the banking union needs only two pillars.
WSJ: In Cyprus Rescue, Germany Forged a New Vision for Bank Union
Mr Van Rompuy's proposed banking union could sever the dangerous link between governments and banks.
Germany is right to say that, in the end, banking union is the start of fiscal union.
An alternative would be for the banking union to apply only to countries in the euro area.
This month the Commission - the EU's executive arm - has released a blueprint for a banking union.
She has got a single bank supervisor for all eurozone banks, a major step towards a banking union.
One of the major attractions is that a eurozone banking union would avoid investor flight or bank runs in one country.
You might have been under the impression that the move to "banking union" was supposed to do just that.
She said European banking union was a key first step to putting Europe on the path to sustainable recovery.
The agreement - a key step towards banking union - will be put before European leaders later on Thursday.
Europe has committed itself to a banking union - and a European supervisor of the eurozone's big banks.
Given more urgent priorities in Europe writing new capital standards, for example, and hammering out a banking union that seems sensible.
As we have argued, that means a detailed plan to build a banking union and to mutualise some debt.
She has previously warned against rushing into banking union out of concern that Germany would face further financial demands.
And so it has proved - with the Bundesbank signalling its opposition to a banking union of this sort.
To make a banking union work, the euro zone will have to create more than just a central supervisor.
He wants a European banking union that contains a joint deposit guarantee scheme.
By injecting their funds directly into Spain's banks, European rescuers could have taken a first step towards a banking union.
The heads of state and government reached three key agreements on bailout funds, moves towards banking union, and on growth.
He favours a banking union, with not just central supervision of big banks but with joint guarantees for banking deposits.
Mr Cameron said Britain and others had demanded proper safeguards in the banking union for countries outside the new arrangements.
"There is no way that Britain is going to be part of any eurozone banking union, " he told BBC Radio 4's Today programme.
BBC: Eurozone crisis: Cameron backs euro but opposes more integration - BBC News
But a euro-area banking union would risk a fragmentation of Europe's single market that might leave Britain's financial industry isolated.
The germ of a banking union is the most likely outcome of the European summit on June 28th and 29th.
While it may have seemed the talks on banking union were going nowhere, last night was a genuine step forward.
The OECD used the outlook to call for bolder measures solve the crisis and faster movement toward a full-fledged banking union.
The European Council looks set to approve the first stage of a eurozone banking union at its meeting in late June.
The eurozone countries are moving towards a banking union, which will give the ECB a central role in regulating the sector.
At the Brussels meeting, eurozone leaders agreed to start building a banking union on 1 January to speed up economic integration.
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