EU Commission President Jose Manuel Barroso has called for the EU to evolve into a "federation of nation-states".
Addressing the EU parliament in Strasbourg, Mr Barroso said such a move was necessary to combat the continent's economic crisis.
He said he believed Greece would be able to stay in the eurozone if it stood by its commitments.
Mr Barroso also set out plans for a single supervisory mechanism for all banks in the eurozone.
He called the plans a "quantum leap... the stepping stone to the banking union".
The European Central Bank would get much greater powers of oversight and regulation of Europe's 6000 banks under the plan.
Mr Barroso said eurozone countries should not rely on bailouts from the ECB, saying the bank "cannot and will not finance governments".
"But when monetary policy channels are not working properly, the commission believes that it is within the mandate of the ECB to take the necessary actions — for instance, in the secondary markets of sovereign debt," he added.
With respect to Greece, Mr Barroso said he believed the eurozone had reached a "turning point".
The inability of governments thus far to respond effectively to economic developments was "fuelling populism and extremism in Europe and also elsewhere", he added.
The banking union would be a big first step in the creation of closer union within the eurozone, the BBC's Chris Morris in Strasbourg reports.
There will be opposition to the plans — the German government, for example, says far fewer banks should be involved, our correspondent says.
Britain does not want to take part but supports the idea of a single supervisor for the eurozone, as long as it does not affect the integrity of the wider EU single market, he adds.
Last week Michel Barnier, the EU commissioner in charge of financial regulation, said he hoped such a scheme could be set up by early 2013.