BRUSSELS – Europe’s government-debt crisis, which has dragged on for more than two years, is entering a pivotal week, as leaders across the continent converge to prevent a collapse of the euro and a global financial panic that could result.

Expectations are rising that Friday’s summit of leaders of the 27 countries in the European Union will yield a breakthrough. An agreement on tighter integration of the 17 EU countries that use the euro — especially on budget matters — would be seen as a crucial first step. That could trigger further emergency aid from the European Central Bank, the International Monetary Fund or some combination, analysts say.

The coming days “will decide if the euro will survive or not,” Emma Marcegaglia, the head of Italy’s industrial lobby, Confindustria, said Sunday.

French President Nicolas Sarkozy, German Chancellor Angela Merkel, European Central Bank Chief Mario Draghi and even U.S. Treasury Secretary Timothy Geithner will star in a five-day financial drama leading up to the summit.

If the summit is a failure, Sarkozy warned last week, “the world will not wait for Europe.”

Sarkozy and Merkel meet in Paris today to unveil a proposal for closer political and economic ties between the 17 euro countries. While the leaders differ on some of the details, their cooperation has been so tight they have come to be known by a single name — “Merkozy.”

The two agree overall on the need for tougher, enforceable rules that would prevent governments from spending or borrowing too much — and on certain penalties for persistent violators.

“Where we today have agreements, we need in the future to have legally binding regulations,” Merkel said Friday.

Merkel wants to change the basic EU treaty to reflect the tougher rules on euro countries and make them enforceable. Even if there is general agreement Friday, actually putting new rules in place through treaty changes could take more than a year. And many economists fear the new rules alone would not be enough to halt the rise in Europe’s borrowing costs.

The hope is that a firm expression of intent, however, would reassure the central bank, so that it can make stronger efforts in the short term. That would give governments time to get their finances under better control and make economic reforms that would improve growth.

The urgency has been heightened in recent weeks as Italy and Spain, the continent’s third- and fourth-largest economies, face unsustainable high costs to finance their debts. The yield on 10-year Italian bonds is around 7 percent. Yields above that level forced Ireland, Portugal and Greece to seek bailouts. By comparison, bond yields in Germany, Europe’s largest and most stable economy, are roughly 2 percent.

Italy, whose government debt is equivalent to 120 percent of the country’s annual economic output, needs to refinance $270 billion of its $2.6 trillion of outstanding debt by the end of April.

The size of the problems facing Italy and Spain are considered too large for the existing funds available to the European Financial Stability Facility ($590 billion) and the IMF ($389 billion.) To boost the firepower of the IMF, several economists have proposed that the European Central Bank lend to it.

Last Wednesday, the U.S. Federal Reserve, in coordination with the ECB and four other central banks, sought to give stressed-out European banks some relief. The Fed announced a plan to make it cheaper for banks to borrow American dollars, which is the dominant currency of trade. It was the most extraordinary coordinated effort since October 2008, and it prompted a nearly 500-point rally in the Dow Jones industrial average.

Still, that help did not address the fundamental problem in Europe: unsustainable levels of government debt.

In Italy, Premier Mario Monti had that on his mind as he unveiled his new austerity and gowth measures he said his government of technocrats approved Sunday. They include what he called immediate cuts to the costs of maintaining Italy’s bulky political class as well as significant measures to fight tax evasion. As part of the political cost cuts, Monti said he would forego his salary as premier.

The package also includes measures to spur growth and competition, while aiming to stamp out rampant nepotism. Monti will outline the measures today to Parliament, which must approve them.

The debt loads of countries like Italy and Greece are everyone else’s problem.

Germany’s economy depends heavily on exports. If economic output in the rest of Europe collapsed, demand for German goods would fall sharply. Across the Atlantic, the United States depends on Europe for 20 percent of its own exports. And investors in American banks have worried about their holdings of European debt.

The bigger threat to the U.S. and the global financial system is that Europe’s debt crisis could spiral out of control.

If governments default on their bonds, banks that own them could take a significant hit. It could become difficult for these banks to borrow and nervous depositors could flee with their cash. In the worst case, a global financial panic could be triggered, in which banks all over are too skittish to lend to each other. That would cause a credit crunch that deprives businesses of the short-term financing they depend on for day-to-day operations.

With such fears in the air, the United States is ratcheting up its involvement. Geithner will meet Tuesday in Germany with Draghi and German Finance Minister Wolfgang Schauble. On Wednesday, he travels to France for talks with Sarkozy and the prime minister-elect of Spain, Mariano Rajoy Brey. And Geithner will meet Monti in Milan just before the new Italian leader heads for the EU summit in Brussels.