Chavez -- who died last month at 58 -- designated his vice president, Nicolas Maduro, to fill out the unexpired portion of his six-year term.
Maduro, the acting president, had a 7-point lead over challenger Henrique Capriles in the most recent major polls -- down from 15 points at the end of March -- the Los Angeles Times said.
Maduro has said he would further what he calls the Chavez revolution, channeling billions in oil revenues into health, food and education programs for the poor, Voice of America reported.
Capriles has labeled Maduro a liar, incompetent and corrupt, and said he plans an aggressive strategy to halt rising inflation, spiraling crime and food shortages, the Times reported.
Chavez died March 5 after a two-year battle with cancer.