The Greek government took a crucial step Tuesday to avoid default, winning parliamentary approval for a highly controversial property tax increase that could help the country meet international conditions for more bailout money.

With global investors showing some optimism that debt problems in Greece and elsewhere in Europe could be resolved, financial markets rose. The German stock market was up 5.3 percent, and the French stock market gained 5.7 percent. U.S. stocks ended the day up 1.1 percent as measured by the Standard & Poor’s 500-stock index. Asian markets were slightly higher in early trading Wednesday. Japan’s Nikkei 225 index ended its morning session up 0.2 percent.

Contributing to the burst of confidence were comments from German Chancellor Angela Merkel, who said in a television interview that she wants Greece to stay in the euro currency area despite the strains caused by the Greek debt crisis.

Also encouraging was the news that the parliament of Slovenia overcame its reservations and backed the proposed expansion of a Europe-wide rescue fund that requires the approval of all 17 nations that use the euro.

The sense of progress toward resolving Europe’s crisis came after days of pressure from global investors and international leaders. Officials from the United States, China and other nations have been urging European governments to act more aggressively to prevent a potential default in Greece from causing a worldwide financial crisis. Over the weekend, U.S. Treasury Secretary Timothy F. Geithner warned of “cascading default, bank runs and catastrophic risk.”

Some European leaders chafed at the remarks, with some worrying aloud that the international pressure has contributed to the atmosphere of crisis. “We always welcome advice from other nations on how to handle this situation,” Andreas Dombret, an executive board member of Germany’s central bank, the Bundesbank, said in an interview. “The advice can be more welcome when it is made in private than in public.”

Greece has said it will run out of money to pay its bills by mid-October if it does not receive more aid. But the country’s European creditors have questioned whether politicians were serious about meeting fiscal targets that were imposed as part of a $150 billion bailout approved in 2010. Tuesday’s actions were intended to help dispel those fears.

The property tax is being imposed in an attempt to raise $2.7 billion in revenue for the deeply indebted government this year and will be imposed through 2014. It hits many families who are already struggling with high unemployment in the private sector and docked wages in Greece’s large public sector.

The tax proposal passed 154 to 143. It will be levied through electricity bills to discourage evasion, meaning those who do not pay risk having their power cut off.

The vote was preceded by small demonstrations outside the Parliament building. Much larger protests and strikes have snarled Athens for days; public transit workers have cut services in an attempt to display their unhappiness over the austerity measures the government has imposed.

But for all that Greece has cut, there is a growing sense among investors and politicians that the country’s debts are too high for it to be able to meet its obligations under the current bailout plans.

Prime Minister George Papandreou dined in Berlin on Tuesday evening with Merkel, who has much say over Greece’s financial fate. In advance of that meeting, Merkel repeated a message she has been delivering for weeks.

“Greece belongs to the euro area, and we want Greece to remain in the euro area,” she told Greek state television.

She acknowledged that the terms of a second bailout agreed to in July may need to be reexamined given the decline in Greek’s economic forecasts, and she said her decision will be based on the findings of an inspection team sent this week jointly by Greece’s creditors: the European Union, the European Central Bank and the International Monetary Fund.

Speaking at a German industry forum Tuesday, Papandreou said that “Greece will live up to all its commitments.”

“We are borrowing to repay,” he said.

Greek Finance Minister Evangelos Venizelos said Tuesday that his country would receive the next $11 billion installment of bailout funds, without which it will run out of money. European officials will decide next month whether to hand over the money.

Irwin reported from Washington.