The French president says a deal to start building a banking union on 1 January will enable the eurozone to speed up economic integration.
"Thanks to this we can advance more quickly and with more assurance," Francois Hollande said in Brussels.
He was speaking after EU leaders agreed to set up a single banking supervisor for the 17-nation eurozone - a key step towards a banking union.
But Mr Hollande also said EU states "need different speeds" of integration.
"We should have a council of the eurozone to meet on a regular basis... We need different speeds - that's agreed by everyone now, and there are even some moving backwards," he told a news conference.
Germany's Chancellor Angela Merkel insisted again that "quality takes precedence over speed" in setting up the banking union.
New ECB clout
It has been agreed that the European Central Bank (ECB), as supervisor-in-chief, will have the power to intervene in any of the eurozone's 6,000 banks.
The deal appears to be a compromise between France and Germany, who earlier disagreed over the timing and over the number of banks the ECB would oversee.
A legislative framework is to be in place by 1 January, with the supervisory body starting work later in 2013.
The timetable remains important, because only when the body is fully operational will the eurozone's new rescue fund, the European Stability Mechanism (ESM), be able to recapitalise struggling banks directly, without adding to a country's sovereign debt pile.
The deal was, at best, an uneasy compromise between the French and Germans and much wrangling lies ahead, the BBC's Europe editor Gavin Hewitt says.
Mrs Merkel insisted on Friday that "the right sequence is important" and added: "It's already quite an ambitious roadmap."
Germany had been at odds with the European Commission over the scope of the proposed ECB supervision. All the eurozone banks will be included - but Germany had wanted it limited to the biggest, "systemic" banks.
Previously, the German government has expressed a desire to retain supervisory responsibility within Germany over the country's Landesbanks - state-owned banks that play a key role in the economies and state finances of Germany's federal regions.
European Council President Herman Van Rompuy said the 27 EU leaders had agreed to set up "a Single Supervisory Mechanism [SSM], to prevent banking risks and cross-border contagion from emerging".
"Once this is agreed, the SSM could probably be effectively operational in the course of 2013," he said.
EU Commission President Jose Manuel Barroso said that the ECB "will be able to intervene if needed in any bank in the euro area".
With new supervisory powers the ECB would be able to act early on to prevent a systemically dangerous accumulation of debt on a bank's balance sheets.
ECB supervision will not extend to the UK - Europe's main financial centre, but outside the euro.
However, the BBC's Business editor Robert Peston says there is now a serious risk that the UK will always be outvoted when decisions are taken on the regulation of banking and finance in the EU as a whole.
It is more than a theoretical possibility that the interests of the UK and City of London in shaping financial rules will be systematically ignored or overridden, he says.
Mrs Merkel said the agreement was that "banks must be supervised in a differentiated way. That means that some will be direct... at the ECB level and others indirectly, via the national authorities."
She also said that ECB President Mario Draghi had told her it would be a matter of some months before the ECB was ready to take on its new role.
Mrs Merkel confirmed that the EU bailout funds would not be used to directly inject risk-absorbing capital into troubled eurozone banks until the new supervisory arrangements were in place.
Fraught with complications
The leaders agreed that the ECB's new supervisory function would be strictly separated from its role in setting monetary policy.
The banking union plan is fraught with legal complications, as it would give more powers to the ECB and possibly weaken those of national regulators.
There is speculation that it could lead to treaty changes - something that has caused big headaches for the EU in the past.
The UK wants safeguards to protect the powers of the Bank of England.
Mr Barroso said the arrangement would be "as inclusive as legally possible for non-euro members to join if they want to".
Source: BBC News