Brussels, Belgium (CNN) -- European leaders must band together to save the euro this week, the leaders of the eurozone's two biggest economies said Thursday, even as the head of the European Central Bank was warning of more bad economic times ahead.
Failure to reach an agreement at a summit in Brussels, Belgium, is a "luxury we cannot afford," French President Nicolas Sarkozy said.
"This is our duty. We have no other choice," he said, warning that the European Union would not get a second chance.
German Chancellor Angela Merkel said countries had to put their "national egotisms" aside and find a joint solution to the continent's debt crisis.
The national debts of euro members, including Ireland and Greece, have pushed the common currency to the brink of collapse, forcing international lenders to swoop in with bailouts.
The budget cuts they have demanded have led to mass protests that brought down governments in both countries -- and they are not the only ones with worrying levels of debt.
The French minister for European affairs, Jean Leonetti, warned earlier Thursday that the euro could "explode" and Europe could "unravel."
That would be a "disaster not only for Europe but for the whole world," Leonetti told the French TV station Canal+ on Thursday morning.
Hours later, the European Central Bank cut a key interest rate to 1%, effective December 14. It's the second cut in the rate in as many months, bringing the rate down to match its lowest level ever.
The head of the bank, Mario Draghi, warned that inflation was likely to stay high in the eurozone and growth would remain low. He announced extraordinary measures to ease financial markets.
But he did not announce that the bank would buy up the debt of eurozone nations struggling to balance budgets, and U.S. stocks fell at the opening.
Germany and France are now pushing for more European Union influence over the national budgets of the countries that use the euro.
Sarkozy and Merkel will present details of their plans at the summit.
But the plans could require all 27 members of the European Union to agree to change fundamental EU treaties -- and British Prime Minister David Cameron has vowed to drive a hard bargain before he will go along.
The United Kingdom is one of 10 EU countries that do not use the euro.
U.S. Treasury Secretary Timothy Geithner has been touring Europe ahead of the summit to underline the importance of the EU's bringing the crisis under control.
"I want to emphasize again how important it is to the United States and to countries around the world that Europe succeeds in this effort to build a stronger Europe, and I'm confident they will succeed," Geithner said in France on Wednesday.
On Thursday he met Italian Prime Minister Mario Monti, who came to power when his country's government collapsed over a debt crisis.
Geithner assured Monti that Washington supported his efforts to balance his country's budget.
Monti said he would meet President Barack Obama in Washington next month.
Some details about another EU plan have already leaked.
European nations could be penalized by being stripped of some powers if they fail to manage their budgets, according to a confidential memo from European Commission President Herman Van Rompuy, leaked Tuesday.
Van Rompuy's proposals may be even stricter than those of Merkel and Sarkozy.
The five-page memo proposes that the European Commission might be given the right to strip voting rights within the European Union from some countries who have been bailed out but are still not meeting their deficit targets.
The executive arm of the EU could force bailed-out countries, such as Greece, Ireland and Portugal, to comply with deficit regulations, which for the entire EU currently stand at 3% of GDP.
The meeting will occur under the shadow of a recent report from the rating agency Standard & Poor's, which threatened to downgrade 15 eurozone member states. Even the AAA-rated nations France and Germany have been placed on review for possible downgrade as the debt crisis continues to worsen.
Two eurozone members were not placed on credit watch -- Greece, because its credit rating already reflects a high risk of default, and Cyprus, which was already under review.
CNN's Naima Benallal reported from Paris; CNN's Jim Boulden reported from Brussels; CNN's Hada Messia reported from Rome, and CNN's Nina dos Santos, Richard Allen Greene and Irene Chapple reported from London.