CARACAS, Venezuela — Faced with a potential erosion of his grip on power as voters went to the polls on Sunday to cast ballots in state and municipal elections, President Hugo Chávez called on his followers and opponents alike to respect the outcome of the races across Venezuela.

“We are prepared to recognize any result,” Mr. Chávez said in televised comments after casting his vote, reminding voters that he quickly conceded defeat in a referendum last year that would have enhanced his powers. Results in 22 states and 328 municipalities, including the Caracas metropolitan area, were expected late Sunday.

Mr. Chávez’s conciliatory tone stood in contrast to threats he has recently leveled, including a warning that he might dispatch tanks to occupy Carabobo, a state with a large industrial base where the political opposition has been gaining strength. He also said he would jail a top political rival, whom he called a “swine,” in western Zulia State.

“I am tired of Chávez treating the entire country as if it were his military barracks,” said Heriberto González, 65, a carpenter, after he voted in Petare, a sprawling patchwork of slums here.

Mr. González said he voted for a slate of opposition candidates including Carlos Ocariz, who was challenging a former interior minister in Mr. Chávez’s government for the mayoralty of Sucre, an impoverished municipality in Caracas that has been a bastion of support for the president since his rise to power a decade ago.

If Mr. Chávez’s candidates lose in Sucre and other areas, a test for Venezuela’s beleaguered political institutions will lie in how the president reacts. Mr. Chávez recently signaled he might move to hand pick new regional authorities, effectively depleting the power of opponents elected by voters. Issues like food-price inflation, which stands above 50 percent, and soaring homicide rates were prominent in campaigning, but elections also revolved around the personality of Mr. Chávez, 54, a former career military official who blames previous governments or the United States, which he regularly calls the “empire,” for Venezuela’s ills.

“We have problems in Venezuela, but I am certain the return of the oligarchy would make them worse,” said Miroslava Toro, 35, a resident of Petare who voted for Mr. Chávez’s candidates. “I know in my heart that Chávez cares about the poor,” said Ms. Toro, a maintenance supervisor at a state health clinic.

Voting unfolded without reports of major irregularities, even if confusion emerged in some areas. In Mr. Chávez’s home state of Barinas, where his family was hoping to maintain its decade-long hold on power, his father, Hugo de los Reyes Chávez, the departing governor, claimed an electronic voting machine switched his choices.

The glitch was reported in televised comments by Mr. Chávez’s older brother, Adán, who was running to replace his father in a bid to fortify a dynasty that has been plagued repeatedly by accusations of corruption and abuse of power. A dissident supporter of Mr. Chávez, Julio César Reyes, competed against Adán in Barinas.