The landslide happened in the early hours of the morning in the village of Nergeti, some 170 kilometres from the Black Sea nation's capital Tbilisi.
"The number of landslide victims rose to six," Georgia's emergency situations service said in a statement, adding that "a search operation is underway to find three missing people."
A previous toll announced four dead.
President Salome Zurabishvili expressed "deep sorrow over the tragic loss of life in the natural calamity".
"I offer my condolences to the families of victims and hope that those missing will soon be found," she said.
The country's National Environmental Agency said the landslide was caused by three days of heavy rains in the area, during which precipitation significantly exceeded the annual norm.
Heavy rains and flooding are fairly common in Georgia, where steep slopes pose a regular risk of landslides.
In August last year, a landslide at a resort town in northwestern Georgia killed 26 people.
In 2008, six people died in a landslide in the southern Black Sea region of Adjara.
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