At least 2,300 have been killed, according to the ambulance authority in Derna, the worst affected city.
Two dams and four bridges collapsed in Derna, submerging much of the city when Storm Daniel hit on Sunday.
About 10,000 people are reported missing, the Red Crescent says, and the death toll is expected to rise further.
Some aid has started to arrive, including from Egypt, but rescue efforts have been hampered by the political situation in Libya, with the country split between two rival governments.
