The leader of the east Libyan government, which is not recognised internationally, said deaths exceeded 2,000 and thousands were missing.
Jalel Harchaoui, a Libya specialist, told the BBC the death toll could reach as many as "several thousand" people.
Storm Daniel made landfall on Sunday, prompting authorities to declare a state of extreme emergency.
Seven Libyan army personnel went missing during ongoing rescue efforts.
Officials in the east imposed a curfew, while schools and shops were ordered to close.