Rivers burst their banks and hillsides collapsed, killing two people in Caracas and five others in isolated incidents across the South American country on Thursday night, a spokeswoman for the emergency services said.
Local authorities used heavy machinery to clear mud and fallen trees from highways and city streets before Sunday's voting.
"We have been working, talking and evaluating for hours and I want to ask the population to stay calm," Chavez said live on television late Thursday. "The government is in action."
In 1999 at least 10,000 people were killed when a mountain collapsed on the Caribbean coast near Caracas on the same day as Venezuelans were voting for a new constitution written by Chavez allies.
There was no rain on Friday morning but forecasters predicted more precipitation in the next 24 hours to 48 hours.
State oil company PDVSA said it had received no reports of problems at its production units or refineries.
Chavez allies run almost all Venezuelan states and cities but are expected to make some losses in Sunday's vote. Government and opposition candidates wasted no time in criticizing each other for their respective responses to the rains, which crushed some houses as mud slid into the valleys of mountainous Caracas. Many neighborhoods there cling precariously to steep slopes.
Caracas ground to a halt on Thursday night as fast flowing water filled rush hour roads. Wet earth squashed several cars.
A pro-opposition television station criticized Chavez for a meeting between his cabinet and Vietnamese officials that was broadcast live on all stations during the rain storm, blocking news coverage for a short time.
Chavez postponed a news conference with foreign correspondents originally set for Friday to focus on the problems caused by the rains.
