According to the ambulance authority in Derna, the city most severely hit, at least 2,300 people have died.
When Storm Daniel slammed Derna on Sunday, two dams and four bridges gave way, burying much of the city beneath water.
The Red Crescent estimates that 10,000 people are missing, and more deaths are anticipated.
Aid has begun to arrive, particularly from Egypt, but the fact that Libya is divided between two competing administrations has made rescue efforts difficult.
Among the nations that have declared they have sent or are prepared to send aid are the US, Germany, Iran, Italy, Qatar, and Turkey
There are terrifying tales of individuals being carried away by the tide as others clung to rooftops for dear life.
Hisham Chkiouat, a representative of Libya's eastern administration, said, "I was shocked by what I saw, it's like a tsunami."
According to him, substantial portions of the city of Derna were pulled into the sea when one of the dams south of it collapsed.
"A vast neighborhood has been destroyed; there are many victims, and the number is growing by the hour."
Mr. Al-Dbeibah claimed that the navy and divers were attempting to recover victims from the sea and that rescue workers were having difficulty recovering certain bodies.
He added that an investigation has been started into how the floodwaters were able to wreak such destruction..
The storm on Sunday also had an impact on the cities of Soussa, Al-Marj, and Misrata.
According to specialists in water engineering who spoke to the BBC, it seems likely that the top dam, which is around 12 kilometers (eight miles) from the city, fell first, sending its water downstream towards the second dam, which is located closer to Derna and where neighborhoods were flooded.
According to Raja Sassi, who survived together with his wife and young daughter, "At first we just thought it was heavy rain but at midnight we heard a huge explosion and it was the dam bursting," according to the Reuters news agency.
Noura Eljerbi, a Libyan journalist residing in Tunisia, told the BBC that she only learned that about 35 of her family, who all lived in the same apartment building in Derna, had been killed.
There is a dearth of medical supplies and safe drinking water in Derna, according to rescue worker Kasim Al-Qatani who spoke to BBC Newsnight.
The lone hospital in Derna, he continued, was no longer able to accept patients because "there are more than 700 dead bodies waiting in the hospital and it's not that big."
Since Col. Muammar Gaddafi, Libya's longtime leader, was deposed and killed in 2011, the country has been in political instability. The oil-rich country is now virtually divided between an interim, internationally recognized government that operates out of Tripoli and another one in the east.
The misunderstanding surrounding this, according to Libyan journalist Abdulkader Assad, is impeding rescue attempts.
He told the BBC, "You have people promising help, but the support is not coming. In Libya, there are no trained rescuers or rescue squads. The last 12 years have been dominated by war.
Despite the division, the Tripoli administration has deployed a plane with more than 80 physicians and paramedics, 14 tonnes of medical equipment, and body bags.
According to Brian Lander, the World Food Programme's deputy director for emergencies, there is enough food on hand to feed 5,000 families.
erna is located about 250 kilometers east of Benghazi along the coast and is encircled by the lush Jabal Akhdar region's surrounding hills.
After Gaddafi's overthrow, Islamic State terrorists once established a presence in the city. Years later, the Libyan National Army (LNA), forces loyal to Gen. Khalifa Haftar who is affiliated with the eastern government, drove them out.
The powerful general claimed that eastern officials are presently evaluating flood damage so that roads can be rebuilt and electricity can be brought back to aid with rescue operations.
According to Libya's top news outlet Al-Wasat, a portion of the high death toll can be attributed to the city of Derna's infrastructure not being properly rebuilt and maintained following years of conflict.
"The security chaos and the Libyan authorities' laxity in carrying out close monitoring of safety measures [of the dams] led to the catastrophe," it quoted.