In El Junquito, a mountainous area west of Caracas, residents told Reuters agency they had seen few public officials, while farmers and other residents have been providing basic supplies to the community.
"We are waiting for answers, for debris to be cleaned up, for inspections, for people who have been really affected to be helped," resident Keily Ibarra, 33, told Reuters.
On Monday Rodríguez said more than 25,000 emergency workers, police officers and soldiers had been assisting Venezuelans affected by the earthquakes.
"Every life saved is a victory for hope," she posted on social media platform X.
She has also announced a commission to assess the damage, to be chaired by her brother, National Assembly President Jorge Rodríguez.
Speaking on state television, she said the group would determine who could return home using a colour-coded traffic light system to classify safety. Temporary camps to house those displaced were being set up in the meantime, she added.
The rescued 21-year-old was found in the town of Caraballeda by teams from Venezuela, Mexico, and El Salvador, Salvadoran President Nayib Bukele announced on Monday.
The man, Aaron Levi Cantillo Vargas, is receiving specialised medical care, Bukele said, adding that the rescuers would "continue working with the hope of being able to save more lives".
The UN's resident humanitarian coordinator Gianluca Rampolla Del Tindaro said on Monday that there had been more than 500 aftershocks and that at least 2,500 structures had been affected by Wednesday's initial quakes, most of which had fully collapsed.
The UN was obtaining 10,000 body bags as part of its rescue operation, he added, saying that a rise in the death toll was unavoidable.
"It is very sad and we truly hope that actually the number is going to be smaller than that and that's why we are focusing now on the rescue operation," he said.
Meanwhile more international aid has been pledged. The US has announced more than $300m (£227m) to help Venezuela - an increase from its previous commitment of $150m.
"These funds will provide emergency medical care, food assistance, water and sanitation, shelter, protection, and logistics," the US state department said.
A US frigate, the USS Fort Lauderdale, is currently positioned off the coast of La Guaira. Sailors and Marines are using landing and amphibious craft to deliver aid to the most affected coastal areas.
The Netherlands has also said it is sending a vessel carrying emergency supplies, while China has promised almost $15m in assistance.

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