Venezuela’s interim president, Delcy Rodríguez, has vowed to fight to save “as many people as possible” as the official death toll from the country’s worst earthquake in more than a century almost doubled, but frustration is growing at the perceived sluggishness of the government’s response.

Rodríguez said on Friday the official death toll had risen to 589, with nearly 3,000 people injured.

Speaking during a tour of La Guaira, the most devastated region, Rodríguez said foreign search and rescue groups were starting to arrive in the crisis-stricken South American country. “We offer our solidarity [to families of victims],” she said late on Thursday outside the ruins of an eight-floor seafront hotel that had been obliterated by twin 7.2 and 7.5 magnitude quakes.

But volunteer searchers and the relatives of the many missing voiced exasperation and anger at the lack of an official response as they waited for government teams.

Rotny Bombart, a 33-year-old paramedic, said he had spent five hours hunting for his mother, María Eugenia, in a collapsed tower block in La Guaira called OPP 33. “It has 15 floors. Or rather, it used to, because there’s nothing left of it now,” Bombart said after being treated at a public hospital in the capital, Caracas, for a gash to his right arm sustained during the search.

Bombart said that at first no government emergency workers had appeared at the scene. In their absence, desperate locals seized the initiative, picking their way through the rubble with bare hands and basic tools. “You’re prepared for emergencies, but not for this. Nothing prepares you for this,” he said, recalling seeing dismembered bodies, dead people and children in the wreckage.

Another searcher, Diego González, said he had spent hours digging his 34-year-old cousin, Helari Rodríguez, out of the debris of Residencias Belo Horizonte, an apartment building in a seaside town in La Guaira called Catia La Mar. “It took us four hours to pull her out of the rubble with the help of some friends,” he recalled.

“People are working with their bare hands. Tools are essential. But Catia La Mar is destroyed – very few buildings will have survived,” González added.

On Thursday, the US defense secretary, Pete Hegseth, said that on Donald Trump’s orders he had mobilised troops to “support the Venezuelan people” in their hour of need. “Our mission is clear: save lives and rapidly deliver critical aid where it is most needed,” Hegseth tweeted.

US Southern Command said Marine Corps Maj Gen Kevin J Jarrard had landed in Caracas to oversee the use of “the US military’s unparalleled logistical and operational capabilities” to help with the search. Other countries, including Brazil, Colombia, El Salvador, Mexico, Spain, France, Turkey and Switzerland have offered to send humanitarian aid and rescue teams.

Yet 36 hours after back-to-back earthquakes devastated Venezuela’s northern coast, there is scant sign of government help reaching many areas, exposing how years of economic misrule and corruption left authorities woefully unprepared for a disaster on this scale.

Chaotic footage from the José María Vargas hospital in La Guaira captured the extent to which Venezuela’s public health system withered as Rodríguez’s predecessor, Nicolás Maduro, led the country into economic freefall. Patients could be seen lying on the floor as they waited for treatment in the facility’s parking lot.

Orlando Pérez, a Latin America expert from the University of North Texas at Dallas, said: “It seems they weren’t prepared at all. Natural disasters reveal the true capabilities of a government because you have to respond quickly, you have to respond efficiently, you have to do search and rescue, [and] you have to provide services in situations where it’s difficult. And it seems that the government has been caught flat-footed completely.

“It’s incredible because this is a resource-rich country,” Pérez added. Venezuela boasts the world’s largest proven reserves of oil but under Maduro was plunged into one of the worst peacetime economic crises in modern history.

Pérez said: “Yet you have completely degraded health infrastructure, buildings that were not built to code that collapsed very easily … They have had the resources but they have squandered it. The health infrastructure in particular is very weak. Hospitals lack equipment, they lack medicine – and that is going to cost lives.”

Writing on X, Juan Pablo Guanipa, a prominent opposition politician, questioned why Venezuela’s armed forces were not doing more to help civilian victims. “So far we have not seen real mobilization or action [from the military] in the face of this grave situation that we are facing. We have seen families, neighbours and rescue workers trying to save lives with their own hands,” Guanipa said, adding: “Right now, all of us need to be involved, the armed forces included.”

Pérez said he was puzzled by reports that there had been scant sign of action by Venezuela’s Bolivarian National Armed Forces (FANB).

He said: “What I am hearing from people is that they have not seen large contingencies of FANB personnel and equipment being mobilized … We know that the FANB’s capabilities had been degraded; that it was an armed force that was structured to prevent a coup. That it was top heavy with a lot of brass and not a lot of capability down in the middle and the bottom – and that it was involved in illicit activities.”

But even so, Pérez thought the “lack of coordinated response and presence seemingly of the FANB” was striking.