The stock market tumbled again Friday as doubts about the ability of European leaders to address a spiraling debt crisis on the continent overshadowed President Obama’s new proposal to spur U.S. job creation.

The Standard & Poor’s 500-stock index was off 2.7 percent for the day, and other U.S. indexes saw similar declines. European markets fell even more precipitously, with the French and German stock markets each down about 4 percent as finance ministers from the major industrialized countries gathered in the south of France to discuss how to deal with the spreading financial crisis.

Europe is facing problems that go beyond crisis-stricken nations such as Greece and Ireland, U.S. Treasury Secretary Timothy F. Geithner said in an interview with Bloomberg Television in Marseille.

“I think it is important the Europeans do what they need to do so their problems do not spread and add to the pressures of the world economy as a whole,” Geithner said.

But there were signs that European leaders’ consensus was splintering further. Reflecting the concerns over Europe’s divisions, the value of the euro fell to a six-month low against the dollar.

Juergen Stark, a member of the European Central Bank’s executive board, resigned Friday after raising internal opposition to the bank’s efforts to contain the continent’s debt crisis. In recent weeks, the ECB has been buying large quantities of Italian and Spanish bonds in an effort to prevent borrowing costs for those countries — two of Europe’s largest economies — from spiking to prohibitive levels.

Stark is the second German central banker to step aside. The ECB has been taking steps that are widely unpopular in Germany, where there is deep-seated opposition to bailing out profligate European neighbors. Axel Weber, the head of the German Bundesbank and a leading candidate to head the ECB, stepped down in April after growing uncomfortable with the institution’s policies.

Meanwhile, rumors were rampant in financial markets Friday that Greece could default on its debt as early as this weekend. The price to insure against default of Greek debt soared 16 percent in the market for credit default swaps, showing that investors view default as increasingly likely. Greek Finance Minister Evangelos Venizelos dismissed that prospect.

Greek Prime Minister George Papandreou is scheduled to deliver a televised address to his nation Saturday to defend the broad austerity measures adopted by his government. These steps, which other European countries are demanding as a condition of providing emergency loans to Greece, have sparked widespread and at-times violent protests.

European banks have been bracing for the possibility of huge losses on their holdings of Greek government bonds. Bloomberg reported Friday that the German government of Chancellor Angela Merkel is developing a “Plan B” to shore up German banks in case a tentative agreement over a new European bailout for Greece falls through and Athens defaults. The report helped send German stocks sharply downward, with the Dax plunging more than 4 percent Friday.

The latest turbulence for world markets came despite Obama’s speech Thursday evening unveiling a $447 billion proposal of tax cuts and spending aimed at bolstering anemic U.S. job creation. Obama’s program received generally favorable reviews from economists.

“Is it worth doing?” wrote Nigel Gault, an economist at IHS Global Insight. ”Yes, it is a bolder-than-expected attempt to inject fiscal stimulus to support an ailing recovery.”

But with the the president’s program facing uncertain prospects in Congress, it was the European crisis that dominated investors’ thinking, analysts said. Money gushed into investments that are considered especially safe, including U.S. Treasury bonds. As demand soared, interest rates on 10-year Treasurys reached their lowest level since at least the 1960s, falling one point to 1.9 percent.

The movement in European bond markets was even more dramatic. Interest rates fell sharply for bonds issued by governments viewed as having sound finances, particularly France and Germany, but soared for weaker countries, such as Italy and Spain.

Stark, 63, who effectively doubled as the ECB’s chief economist for more than five years, cited “personal reasons” for stepping down, according to a short statement issued by the bank. But reports out of Frankfurt indicated that Stark was bitterly at odds with the ECB’s program to aid Italy and Spain by buying up tens of billions of dollars’ worth of hard-hit government bonds.

Also Friday, Merkel made her most explicit call yet to bind the European Union closer together to keep the euro stable, calling on the E.U. to amend its governing treaties and move toward a more common economic policy, Bloomberg reported.

“If the world changes, you have to be ready at all times to make the required changes in such a union,” Merkel said at a policy forum in Berlin. She did not make specific proposals or say what steps might be required.

Analysts said another German economist, Deputy Finance Minister Joerg Asmussen, was a leading candidate to succeed Stark.

“They are replacing one hawk with another hawk,” said Simon White, a partner with London-based Variant Perception. White said it was unclear whether Asmussen, if tapped, would continue to oppose the bond-buying program.

Germany, the largest economy in the 17-nation euro zone, has become increasingly hesitant about its role in the bailouts as angry taxpayers have been forced to bear the highest burden of the rescues.

Stark’s resignation underscored the sharply divided nature of the campaign to bolster Italy in particular and prevent a full-blown debt crisis in the euro zone’s third-largest economy. Euro-zone leaders are continuing talks on an expanded bailout package for Greece, which has been hampered by Finland’s demand for collateral in exchange for the loans.

Faiola reported from London.