Hidalgo state governor Omar Fayad announced that the toll had increased to 73 after the discovery of five additional bodies.
The blast -- which Fayad said injured 74 people -- occurred near Tlahuelilpan, a town of 20,000 people about an hour's drive north of Mexico City.
As soldiers guarded the devastated, still-smoking scene, forensic specialists in white suits worked among the blackened corpses -- many frozen in the unnatural positions in which they had fallen -- and grim-eyed civilians stepped cautiously along in a desperate search for missing relatives.
The pungent smell of fuel hung in the air. Fragments of burnt clothing were strewn through the charred brush.
When the forensic workers began attempting to load corpses into vans to be transported to funeral homes, some 30 villagers tried to stop them. They demanded their relatives' bodies, saying funeral homes were too expensive. The bodies were ultimately taken to a morgue, authorities said.
On Friday, when authorities heard that fuel traffickers had punctured the pipeline, an army unit of about 25 soldiers arrived and attempted to block off the area, Defense Secretary Luis Crescencio Sandoval told reporters.
But the soldiers were unable to contain the estimated 700 civilians -- including entire families -- who swarmed in to collect the spilled gasoline in jerrycans and buckets, witnesses said.
The armed soldiers had been moved away from the pipeline to avoid any risk of confrontation with the crowd when the blast occurred, some two hours after the pipeline was first breached, Sandoval said.
President Andres Manuel Lopez Obrador, a leftist who took office only weeks ago, traveled to the scene early Saturday.
He did not fault the soldiers, saying, "The attitude of the army was correct. It is not easy to impose order on a crowd." He vowed to continue fighting the growing problem of fuel theft.
"I am deeply saddened by the suffering in Tlahuelilpan," Lopez Obrador wrote on Twitter. He called on his "whole government" to extend assistance.
The US Secretary of Homeland Security, Kirstjen Nielsen, tweeted that her department "stands ready to assist the first responders and the Mexican government in any way possible."
Video taken in the aftermath showed screaming people fleeing the scene as an enormous fire lit up the night sky.
"I went just to see what was happening, and then the explosion happened. I rushed to help people," Fernando Garcia, 47, told AFP. "I had to claw through pieces of people who had already been burned to bits."
The tragedy comes during a highly publicized federal government war on fuel theft, a problem that cost Mexico an estimated $3 billion in 2017.
Acting attorney general Alejandro Gertz described the latest disaster as "intentional" because "someone caused that leak. And the fire was a consequence of the crime."
But he acknowledged that investigators would be hampered by the fact that "the people closest to the explosion died."
Federal and state firefighters and ambulances run by state oil company Pemex rushed to help victims with burns and take the injured to hospitals.
Local medical facilities struggled to cope with the flood of arriving victims, said AFP correspondents at the scene.
The fire had been brought under control by around midnight Friday, the security ministry said.
Pemex said it was also responding to another fire at a botched pipeline tap in the central state of Queretaro, though in that case there were no victims.
Mexico is regularly rocked by deadly explosions at illegal pipeline taps, a dangerous but lucrative business whose players include powerful drug cartels and corrupt Pemex insiders.
Fayad said that two hours after the pipeline was punctured, "we were informed that there had been an explosion" and the flames "were consuming everything around."
About 15 oil pipeline explosions and fires causing more than 50 fatalities each have occurred around the world since 1993. Most were in Nigeria, where in 1998 more than 1,000 people died in such a blast. A fire after a pipeline rupture in Brazil killed more than 500 people in 1984.
Rampant fuel theft
The tragedy comes as anti-corruption crusader Lopez Obrador presses implementation of a controversial fuel theft prevention plan.
The government has shut off major pipelines until they can be fully secured and deployed the army to guard Pemex production facilities.
But the strategy to fight the problem led to severe gasoline and diesel shortages across much of the country, including Mexico City, forcing people to queue for hours -- sometimes days -- to fill up their vehicles.
The president, who took office on December 1, has vowed to keep up the fight and asked Mexicans to be patient.
At the scene, some locals blamed the shortages for the tragedy.
"A lot of people arrived with their jerrycans because of the gasoline shortages we've had," said Martin Trejo, 55, who was searching for his son, one of those who had gone to collect the leaking fuel.
He also lashed out at the army for failing to stop the looters.
"These lives would have been saved if they had done their jobs to remove people and not let them get close. They never did anything."
Tanker trucks are being used to deliver fuel, but experts say there are not nearly enough of them.
Mexican bank Citibanamex estimated Wednesday that the shortages would cost Latin America's second-largest economy around $2 billion, "if conditions return to normal in the coming days."
The roots of the fuel theft problem run deep in Mexico, where the practice -- known locally as "huachicoleo," or moonshining -- is big business for some communities.