"It is very hard for us to identify them because some of the dead lost their features or their fingerprints" from the red-hot flows, said Fanuel Garcia, director of the National Institute of Forensic Sciences.
Fuego has been erupting since 2002, and was continuously active in 2017.
There is no electricity in the hardest hit areas of Los Lotes and El Rodeo, so most searching continued only until sunset.
Few of the bodies have yet been identified because the intense heat left them unrecognizable.
By Monday, the intense activity had subsided, Conred said.
The head of the country's disaster agency had previously put the death toll at 33, but warned it would go higher. Pyroclastic flows [or surges] can move at over 100km per hour, and may not be hot enough to glow like molten lava.
Aviation authorities closed Guatemala City's worldwide airport because of the danger posed to planes, but the airport was reopened at mid-morning Monday after workers cleared away ash.
Flights to and from Guatemala City's La Aurora airport were canceled, leaving thousands of travelers stranded. However, the airport press office says each airline is free to make its own decision about whether to resume flights. There were explosions and ash plumes and a volcanic mudflow last month.
The runway was closed due to the presence of volcanic ash, Guatemala's civil aviation authority said in a tweet.
"We hope it will not mean a secondary disaster", he said.
"The landscape on the volcano is totally changed, everything is totally destroyed", government volcanologist Gustavo Chigna said on local radio.
A group of residents arrived at the scene with shovels and work boots.
More than 3,100 people have been evacuated while search and rescue efforts continue into the night, said Sergio García Cabañas, director of the disaster agency.
Volcan del Fuego had already erupted once this year, and it is one of the most active volcanoes in Central America.
The eruption killed at least 25 people and injured many more.
Israel and Guatemala have grown increasingly close in recent years.
On May 21 Paraguay became the third country to open its embassy in Jerusalem. Palestinians seek East Jerusalem as their future capital and have been infuriated by the embassy moves.
Volcan de Fuego, which translates to "volano of fire" exploded just before noon on Sunday, 27 miles from Guatemala City.
At least seven people, including three children, were killed and almost 300 injured on Sunday in the most violent eruption of Guatemala's Fuego volcano in over four decades, officials said.
Authorities said at least six people were dead or missing following the eruption. Hundreds of rescue workers rushed in to try to tend to the badly injured and help anyone still alive, but they struggled to reach some of the rural villages. Rescue workers expect the death toll to rise in the coming days as they reach some of these other towns.