National assembly head Jorge Rodriguez said in a state TV broadcast on Friday that the death toll had reached 920, with at least 172 people still believed to be trapped.
In La Guaira alone, at least 243 people have been rescued, the top lawmaker - who is the interim president's brother - said.
Dozens of people have been rescued alive, which "brings us joy that they can embrace their families and loved ones", Acting President Delcy Rodríguez said at a televised briefing on Friday.
There have been 214 aftershocks since the initial quakes, she added.
On Saturday, the UN's Tom Fletcher told BBC Radio 4's Today programme teams were surging in, as the first 72 hours after the earthquake were "crucial".
"It's absolutely grim, it's devastating and for us we are driven on minute by minute, hour by hour, by the sound of the survivors underneath the rubble."
"We cannot pause for a second while we hear them, but the worst thing is when those voices go quiet. We're determined to save as many lives as we can."
There are reports of rescuers pulling people out of collapsed buildings with their bare hands, as disrupted communications, damaged roads, and a lack of resources made the initial emergency response difficult.
Fletcher said the UN has 39 search and rescue teams deployed, with each consisting of 50-100 people.
"You're looking at almost 2000 people surging in, 111 dogs, medical teams as well. We go in with these micro drones, they call them cockroach drones, that help us find people in the buildings."
A UK military flight carrying British search and rescue teams, dogs and drones left RAF Brize Norton in Oxfordshire on Friday, bound for Venezuela.
The flight is carrying specialists from 14 UK fire services, led by Merseyside Fire and Rescue.
Other countries, including the United States, the Netherlands, Mexico and Switzerland have sent teams. The US has also announced the deployment of warships and transport planes as well as $150m (£113m) in aid.
A BBC reporter in Caraballeda, in La Guaira state, has seen heavy machinery arrive to begin the task of removing rubble.


