Chavez's political allies framed the election as a referendum on his legacy, urging people to dedicate the vote to the president. The government put up banners on lampposts reading "Now more than ever, with Chavez."
Jorge Arreaza, Chavez's son-in-law and the government's science and technology minister, said in a Sunday phone call from Havana broadcast on television that Chavez was continuing to recover and that there has been "a positive trend of stabilization."
"'El Comandante' has begun to communicate with us, to give instructions, to govern," Arreaza said, adding that Chavez was closely following the elections.
Chavez's four children have been with him while he recovers from the surgery, his fourth operation related to his pelvic cancer since June 2011.
Ricardo Mendez, a bus driver who voted for Jaua, said he was optimistic but also noted that few people were voting. "It seems like people are more interested in getting ready for Christmas than anything else," he said.
Baker Luis Chacon, who also voted for Jaua, said he still thinks Chavez can beat cancer and isn't particularly concerned about what would happen if he doesn't. "If he gets worse, new elections will come to choose another," Chacon said, after voting in the working-class slum of Petare.
If the Chavistas make gains or even hold steady, the executive branch could strengthen its hold on the grass roots, as communal councils decide such questions as who gets a new roof, or which streets need repairs, distributing the funds directly. Chavez's opponents have objected to the government's campaign to develop such state-funded "communes" because they bypass the traditional authority of state and local elected officials.
Chacon said that while he supports Chavez, the local communal council has no presence where he lives and hasn't managed to fix broken lights and stairs that wind through the hillside slum.
Voters in some areas of Caracas were awakened before dawn by fireworks and reveille blaring from speakers mounted on trucks.
But the closeness of the vote to Christmas and apparent apathy among many voters appeared to contribute to a low turnout. In the last presidential election, more than 80 percent of registered voters turned out, but gubernatorial elections tend to draw fewer people.
Some said a low turnout was a potential hazard both for Chavez's camp and the opposition.
Political analyst Carlos Raul Hernandez said he thinks Chavez's illness could keep some voters away because he's developed "a style of messianic leadership" in which he stands out far above his political allies.
"There are a lot of people who are only interested in Chavez, not at all the governors," Hernandez said.
Associated Press writers Christopher Toothaker and Vivian Sequera contributed to this report.