Around 1330 GMT, the national telecom company the Libyan Post Telecommunications & Information Company, or the LPTIC, which had earlier confirmed the service cut, said on its Facebook page that it was "gradually" restoring communication to the eastern regions.
Communication was "restored to the eastern regions after the cuts in the cables," the statement said, adding that "work is still ongoing to restore the rest of the routes."
VOA spoke with residents in Derna who confirmed communications have been restored, but said connection remained unstable.
A tsunami-sized flash flood broke through two ageing river dams upstream from the city on the night of September 10, razed entire neighborhoods and swept an untold thousands into the Mediterranean Sea.
On Monday, protesters massed at the city's grand mosque, venting their anger at local and regional authorities they blamed for failing to maintain the dams or to provide early warning of the disaster.
"Thieves and traitors must hang," they shouted, before some protesters torched the house of the town's unpopular mayor.
On Tuesday, phone and online links to Derna were cut, an outage the national telecom company LPTIC blamed on "a rupture in the optical fibre" link to Derna, in a statement on its Facebook page.
The telecom company said the outage, which also affected other areas in eastern Libya, "could be the result of a deliberate act of sabotage," and pledged that "our teams are working to repair it as quickly as possible."
Rescue workers have kept digging for bodies, with the official death toll at around 3,300 but many thousands more are missing since the flood sparked by torrential rains from Mediterranean Storm Daniel.
The huge wall of water that smashed into Derna completely destroyed 891 buildings and damaged over 600 more, according to a Libyan government report based on satellite images.
Some information for this report came from Agence France-Presse. This story has been updated to include VOA's reach to local residents.