Days of torrential rain and melting snow have caused the worst floods in Georgia for many years.
Hundreds of homes have been evacuated because of the floods
The flooding has hit about one-third of the country, leaving villages isolated. Hundreds of houses have been evacuated.
Roads, power lines and communications have been damaged by the flood waters and further rainfall is expected.
Greece, the United Nations, and other international organisations have offered assistance to Tbilisi, which is also braced for more flooding.
Gigi Ugulava, chief of the presidential administration in the Georgian capital, said the Mtkvari River in Tbilisi had overflowed its banks in areas.
"But at least there won't be rain everywhere at the same time - that gives us reason to hope," he told the Associated Press.
Officials say districts in the mountainous region of Svaneti, as well as the western Tsageri district, have suffered.
Some countries and organisations have offered aid to Georgia
President Mikhail Saakashvili, visiting the Shida Kartli region in central Georgia, said millions of dollars would be needed to repair roads and bridges damaged by the floods throughout Georgia.
"Georgia has not faced such a great amount of damage for the past decade," he said.
The breakaway region of South Ossetia has reportedly rejected an offer of aid from Mr Saakashvili.