The floods were caused by torrential rains from Storm Daniel.
Libya's eastern city of Derna was counting its dead Wednesday with 2,300 people confirmed killed in devastating flash floods unleashed by Storm Daniel and the Red Cross warning that 10,000 are missing.
Two river dams burst after the storm hit on Sunday afternoon, releasing an enormous surge of water that tore through the Mediterranean coastal city, sweeping away buildings and the people inside them.
By late Tuesday, the confirmed death count from emergency services in the politically fractured North African country was at least 2,300, although some officials were quoted as giving figures more than twice as high.
Another 10,000 people were still missing, said Tamer Ramadan of the International Federation of Red Cross and Red Crescent Societies.
"The death count is huge and might reach thousands," Ramadan said.
"We don't have a definite number right now," he said on Tuesday, stressing though that the organisation had independent sources saying "the number of missing people is hitting 10,000 persons so far".
Media reports quoted a spokesman for the interior ministry of Libya's eastern-based government as saying "more than 5,200" people had died in Derna.
The city of Derna, a 300-kilometre (190 mile) drive east of Benghazi, is ringed by hills and bisected by what is normally a dry riverbed in summer, but which became a raging torrent of mud-brown water that also swept away several major bridges.
Derna was home to about 100,000 people, and many of its multi-storey buildings on the banks of the riverbed collapsed, with people, their homes and cars vanishing in the raging waters.
With global concern about the disaster spreading, several nations offered urgent aid and rescue teams to help the war-scarred country that has been overwhelmed by what one UN official called "a calamity of epic proportions".
Elsewhere in eastern Libya, aid group the Norwegian Refugee Council said on Tuesday that "entire villages have been overwhelmed by the floods and the death count continues to rise".
"Communities across Libya have endured years of conflict, poverty and displacement. The latest disaster will exacerbate the situation for these people. Hospitals and shelters will be overstretched."
Oil-rich Libya is still recovering from years of war and chaos that followed the 2011 NATO-backed popular uprising which toppled and killed longtime dictator Moamer Kadhafi.
The country is divided between two rival governments -- the UN-brokered, internationally recognised administration based in Tripoli, and a separate administration in the disaster-hit east.
Rescue teams from Turkey have arrived in eastern Libya, according to authorities. The United Nations and several countries offered to send aid, among them Algeria, Egypt, France, Italy, Qatar and Tunisia.
France is sending a field hospital and around 50 military and civilian personnel able to treat 500 people a day, Paris said on Tuesday.
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