The first emergency teams on the scene in Badakhshan province started digging through rocks and dirt as local authorities, the United Nations and the NATO-led military force raced to assess the damage and provide help.
"The number of deceased has increased to 350," the UN mission in Afghanistan said in a statement.
"A response is being mobilised for those who survived but were displaced, with some partners already on the ground.
Badakhshan is a remote province in northeast Afghanistan bordering Tajikistan, China and Pakistan.
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"It is a disaster. The landslide has affected around 1,000 families," Sayed Abdullah Homayun Dehqan, provincial director of the Afghan National Disaster Management Authority, told AFP.
"Around 300 families are missing, that could involve around 2,000 people. The people are working to remove the rocks, so far three bodies have been recovered.
"Around 700 families were rescued, we have sent in some basic assistance such as tents and blankets."
"We stand ready to help our Afghan partners as they respond to this disaster," Obama said at a joint press conference in Washington with German Chancellor Angela Merkel.
The UN said that it was helping to coordinate local authorities to rescue those still trapped, but that road access to the area could not take heavy machinery.
"About 350 to 400 houses were destroyed in Argo district as a result of heavy rains that triggered landslides," Badakhshan province deputy governor Gul Mohammad Baidaar told AFP.
"With nearly 3,500 houses reported damaged and destroyed the caseload in need of shelter continues to grow," the United Nations Office for the Coordination of Humanitarian Affairs (OCHA) said yesterday.
It said clean water, medical supplies, food and shelter were needed immediately as relief efforts were stepped up after days of torrential rain.