NEW YORK — Stocks surged Friday, erasing their losses for the week, after Italy and Greece moved closer to getting their financial crises under control. The Dow Jones industrial average jumped back above 12,000.

Italy’s benchmark stock index leapt 3.7 percent and its borrowing costs plunged after the country’s Senate passed a crucial austerity budget demanded by the European Union. Other European stock markets and the euro also pushed higher as investors became more confident that Italy would avoid a fiscal disaster.

The passage clears the way for Italian Premier Silvio Berlusconi to step down. Berlusconi was widely considered an obstacle to serious economic reforms. The yield on Italy’s benchmark two-year bond dropped 0.43 percentage point to 5.69 percent. That’s a sign bond investors think Italy will succeed in managing its massive debt load. On Wednesday the yield soared as high as 7.13 percent.

The Dow Jones industrial average jumped 259.89 points, or 2.2 percent, to 12,153.68. It closed below 12,000 the previous two days. Friday’s rally pushed the Dow up 1.4 percent for the week.

Together with a 112-point gain the day before, the Dow has now made up most of the 389-point plunge it took on Wednesday. That sell-off was triggered by the spike in Italy’s borrowing costs and a breakdown in talks to name a new prime minister in Greece.