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.
The US, Germany, Iran, Italy, Qatar and Turkey are among the countries that have said they have sent or are ready to send aid.
Video footage recorded after dark on Sunday shows a river of floodwater churning through the city with cars bobbing helplessly in the current.
There are harrowing stories of people being swept out to sea, while others clung onto rooftops to survive.
"I was shocked by what I saw, it's like a tsunami," Hisham Chkiouat, from Libya's eastern-based government, said.
He told BBC Newshour that the collapse of one of the dams to the south of Derna had dragged large parts of the city into the sea.
"A massive neighbourhood has been destroyed - there is a large number of victims, which is increasing each hour."
Mr Al-Dbeibah said rescue teams were struggling to recover some bodies, and that the navy and divers were trying to retrieve bodies from the sea.