CARACAS— President Rafael Correa of Ecuador swept to re-election on Sunday in a vote that showed the broad popularity of his government’s social programs and support for the poor in a country to which he has brought stability after years of political and economic turmoil. With about three-quarters of the ballots counted on Sunday evening, Mr. Correa had received 56 percent of the votes cast. Guillermo Lasso, a banker, the closest of his seven opponents, had 23 percent. Thousands of supporters in the main square in Quito, the capital, began celebrating shortly after voting finished at 5 p.m., when television stations announced the result of exit polls showing Mr. Correa as the runaway winner. "Many thanks for this immense trust,” Mr. Correa said from the balcony of the presidential palace. "We have never failed you, and we never will fail you.” Critics of Mr. Correa have worried that such a strong mandate would embolden him to further concentrate power and proceed with policies that could limit press freedom and quash dissent. Following the re-election last fall of President Hugo Chávez in Venezuela, Mr. Correa’s victory ratified the lasting appeal in the region of leftist governments that have used revenues from booming oil and mining industries to finance social welfare programs aimed at redistributing wealth and curbing inequality. Now, with Mr. Chávez battling cancer, Mr. Correa could raise his profile as one of the most vocal leaders on the Latin American left. Mr. Correa told reporters that he would continue policies aimed at ending poverty and diminishing inequality, saying the challenge of the next four years "is go faster and deeper in the same direction.” His victory also highlighted the weakness of the political opposition in Ecuador. He faced a raft of opponents from across the political spectrum who split the vote from a fractured opposition that was unable to coalesce behind a single candidate or project a unified message. Mr. Correa also won points from voters for bringing stability to Ecuador, a country that had seven presidents in the decade before he took office and was buffeted by severe economic problems. According to the new Constitution that was passed at his urging in 2008, Mr. Correa cannot run again when his new term ends in 2017. Mr. Correa, an economist who studied at the University of Illinois, has improved access to education and health care for the poor and has built or improved thousands of miles of roads and highways. In a new term, he has pledged to continue signature social programs and to pass laws covering the news media, land reform and the penal code.