Mr. Maduro has indicated that he intends to pick up where Mr. Chávez left off. He has suggested a nine-point outline that includes increasing public spending for education and health care, giving Socialist organizations increased governing abilities and taking unspecified measures to prevent foreign meddling in Venezuela.

Analysts also expect that the new Constitution could dig deeper into the economic policy favored by the president, which many economists blame for exacerbating the country’s economic crisis.

With much of the opposition expected to boycott the vote, it was mainly Venezuelans loyal to Mr. Maduro’s party who were eager to head to the polls on Sunday.

María Elena Pérez, 54, a leftist activist in Caracas, the capital, said it was time for a new rule book.

“The current Constitution is weak, and there’s a lot that needs to be fixed,” she said.

In the week ahead of the vote, potential delegates were making their pitches on Venezuelan airwaves.

In one video, Ysmael Modoy, a candidate from the western state of Portuguesa, urged voters to defend Mr. Chávez’s legacy and promised a new Constitution that better battled corruption.

Some sought a lighthearted tone. Antonio León, a candidate who goes by the nickname the Mask, entered his commercial dancing and singing while crossing an empty street. He didn’t address any changes to the Constitution, but promised voters that he would make it easier to get government rations.

“Remember: You are love, you are life,” he said before returning to his dance.