At least 30,000 people have been displaced in the town hardest hit by floods in Libya.
Health officials said the death toll in the city of Derna has risen to more than 5,100 - while a minister has said 5,300 bodies in the country's east have been recovered.
The number of fatalities is expected to rise significantly.
On Wednesday, the UK government announced an initial aid package worth up to £1m to meet the immediate needs of those affected by the catastrophic flooding in Derna.
Prime Minister Rishi Sunak said in a tweet it is "shocking to see the scale of the loss and devastation caused by the floods in Libya", adding that the UK is "working to provide immediate assistance to the Libyan people".
It comes after Libyan officials appealed for international help, warning that the country doesn't have the necessary experience to deal with a disaster of this scale.
Storm Daniel caused significant damage to roads and telecoms networks on Sunday - with strong winds and sudden heavy rainfall devastating the port city of Derna - about 560 miles (900km) east of the capital, Tripoli.
The "sea is constantly dumping dozens of bodies", Hichem Abu Chkiouat, minister of civil aviation in the administration that runs eastern Libya, said, adding that reconstruction would cost billions of dollars.
"We have counted more than 5,300 dead so far, and the number is likely to increase significantly and may even double because the number of missing people is also thousands," he said.
Footage of one man, described by the charity Libyan Red Crescent Society as a grieving father, showed his distress as his son's body was recovered from a collapsed building and prepared for transportation.
"May God make your reward great. Remember God. There is no God but God. May God grant you patience," one of the rescuers said.
The father replied: "Keep them there, don't carry them at all. I will do it."
"Our hearts are with you, we're all with you," the rescuer said.
As Storm Daniel pounded the coast on Sunday night, Derna residents said they heard loud explosions when dams outside the city collapsed.
Floodwaters washed down the riverbed, which runs from the mountains through the city and into the sea.
Waves measuring seven metres (23ft) high "destroyed everything in their path", Yann Fridez, head of the delegation of the International Committee for The Red Cross in Libya, told France24.
"The human toll is enormous," he said.
Rescue teams are still trying to recover bodies scattered in the streets and under rubble in the city, as at least 10,000 people were still missing, according to Tamer Ramadan, Libya envoy for the International Federation of Red Cross and Red Crescent Societies.
Ahmed Abdalla, a survivor who joined the search and rescue effort, said they were putting bodies in the garden of a local hospital before taking them for burial in mass graves at the city's only intact cemetery.
Libya's neighbours, Egypt, Algeria and Tunisia, as well as Turkey and the United Arab Emirates, have sent rescue teams and humanitarian aid.
British Foreign Secretary James Cleverly said on Tuesday: "My thoughts are with all those affected by the catastrophic flooding in eastern Libya. The UK stands ready to provide assistance. We are in contact with the Libyan authorities and the UN to urgently assess what support we can provide to help the Libyan people at this tragic time."
President Joe Biden also said the United States is sending emergency funds to relief organisations and coordinating with the Libyan authorities and the UN to provide additional support.
But the arrival of aid has been hampered due to the destruction of roads leading to the city. Bridges over the river Derna that link the city's eastern and western parts have also collapsed, according to the UN's migration agency.