Jorge Rodríguez, the president of Venezuela’s National Assembly, said 250 buildings had been damaged or lost, mostly in La Guaira.
Photos and videos showed debris strewn on the streets. In some footage, people can be heard calling for help.
The BBC has verified footage of a 10-storey hotel reduced to rubble in La Guaira, and another video that recorded people screaming and fleeing as a multi-storey collapses in El Junquito, west of Caracas.
Other verified footage shows destruction further from the capital. One video shows a multi-storey building, reportedly a hotel, totally collapsed in Tucacas, on Venezuela’s coast, about 250km (155 miles) northwest of Caracas.
Mayor Gustavo Duque of Chacao, which forms part of the greater metropolitan area of Caracas, said on Thursday outside the rubble of one collapsed building that 11 people had died there and 23 had been rescued.
In an Instagram video, he said the team was trying to clear the rubble so that specialists could go in “to reach people who are hopefully still alive”.
“We’re trying to rescue as many people alive as possible,” he said.
Fuel supplies into the city have been cut off and internet blackouts have also been reported.