ATHENS—Greeks were casting ballots Sunday in local polls that could trigger a general election unless voters show support for the governing Socialists’ austerity measures in the debt-strapped country.

Prime Minister George Papandreou has vowed to call a snap election if his 13-month-old Socialist government loses public backing for the harsh fiscal reforms required for Greece to receive €110 billion ($154.37 billion) in bailout loans from the European Union and International Monetary Fund.

However, he hasn’t said clearly what results he would consider satisfactory, leaving himself room to maneuver when polls close Sunday night. The Socialists appear unlikely to suffer a heavy defeat, with opinion polls predicting a roughly even split with main opposition conservatives in the 13 regional governor races.

“I have no desire to go to national elections,” Mr. Papandreou said in his last pre-election rally Friday. “But for this massive effort by the country to succeed we must have public unity and dedication when faced with this great challenge.”

The early election threat has spooked bond markets concerned about Greece’s ability to cope with the massive debts that triggered a financial crisis and affected the euro. The uncertainty sent borrowing costs sharply higher, with the interest-rate gap between Greek 10-year bonds and Germany’s benchmark equivalent exceeding 9 percentage points Friday.

Mr. Papandreou came to power in October 2009 with a landslide victory over the conservatives, and his party enjoys a comfortable majority in Parliament. But recent opinion polls have shown his popularity has taken a beating following stringent austerity measures, including freezing pensions and trimming salaries.

A smiling Mr. Papandreou cast his ballot in a northern Athens suburb just before noon. “Today is a day of important decisions,” he said, extolling the far-reaching reforms in local government. “We are also taking decisions for the stability of the course of the country, and we need this stability to continue the self-evident—often difficult, but self-evident—changes.”

“There shouldn’t be elections again, I think,” said Sofia Panagiotopoulou, an 86-year-old voter in Athens. “We are at the edge of the cliff and we will vote for the status quo so that we can have peace of mind.”

Opposition parties all campaigned against the terms of the bailout loans, adding pressure on Mr. Papandreou, who has faced months of strikes and disruptive protests as a deepening recession caused a surge in unemployment and small business failures.

Conservative leader Antonis Samaras urged the government to “change course” and replace austerity with a policy of state investment to stimulate the economy. “The prime minister should visit ordinary people and realize how much they are suffering,” he said in his final campaign appearance Friday.

Gauging the results of Sunday’s election and runoffs on Nov. 14 will be made more difficult by local party alliances and rebel candidacies that are likely to cost the Socialists a victory in greater Athens.

EU and IMF officials are due back in Athens this month for a fiscal inspection. The EU’s statistics service Eurostat is to again revise Greece’s 2009 budget deficit upward, with the figure expected to exceed 15 percent of gross domestic product from the current projection of 13.6%.

Sunday’s election follows reforms in local government that boosted the powers of Greece’s 13 regional governors, who are directly elected for the first time, and reduced the number of municipalities from 1,014 to 325.

Runoffs will be held on Nov. 14.

Polls close at 7 p.m. (5 p.m. GMT), with 9.8 million eligible voters. Early returns are expected after 9:30 p.m. Broadcasters aren’t conducting exit polls, citing budget cuts.

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Papandreou Braces for Austerity Backlash as Greece Holds Local Elections