"As of this moment, 37 bodies have been recovered, but rescue efforts have come to a halt because it rained this afternoon and the orders are to withdraw the rescue crews in such circumstances," said Antioquia department spokesperson Jorge Humberto Salazar.
With scores of people still missing from the mudslide, around 400 rescuers have been toiling since Sunday, with diminishing hopes of finding survivors.
Manual digging in the area on Tuesday gradually gave way to heavy machinery, as rescuers battled a narrowing time window to find people still alive under the mud.
"We're bringing in machines, but only after sniffing dogs rule out the presence of any body in the area," said Salazar.
Officials said a wall of mud slid down a sodden hillside on Sunday, burying about three dozen homes near Medellin, Colombia's second-largest city, 245km northwest of Bogota.
Relocation
The tragedy occurred after a hillside perched above the La Gabriela neighbourhood in the town of Bello gave way.
Santos visited the disaster site earlier and promised his government would do everything in its power to help the victims of the tragedy.
"We've facilitated a number of resources and launched procedures to relocate people who have lost their homes. They will have subsidised rent while new homes are built," he said in Medellin.
Back in in the capital, Santos later said on television: "To deal with emergency situations, you have to also adopt emergency measures. We've decided to declare an economic, social and environmental state of emergency in the disaster area."
Federal aid, he said, will initially focus on the humanitarian situation, "saving lives, provide housing and food to almost 330 000 families that need it".
Colombia has endured the worst downpours in decades which have left nearly 200 people dead and 1.5 million homeless from flooding and landslides.