The commercial plane, operated by Hewa Bora Airways and carrying 118 passengers and crew, crashed at Kisangani airport in the northeast of the country.
"We have recovered 44 bodies and there were two injured who died in hospital, bringing the number of dead to 46," Hewa Bora president Stavros Papaioannou said, adding that the toll could rise.
The company head said the crew of the Boeing 727 were among those killed but that 53 people had survived the crash.
There was no word on the fate of the other 19 people on board.
"They arrived at Kisangani, there was bad weather, they tried to land without reaching the runway," he said, adding that heavy rains at the time had hampered the rescue operation.
The plane was on its regular commercial route from Kinshasa to Kisangani and Goma when it was hit by the storm as it approached the airport, Lambert Mende, a spokesman for the local administration said.
A plume of black smoke could be seen at the end of the runway, an AFP journalist reported. But flights, which had been suspended after the crash, resumed a short time later.
Hewa Bora said the plane was carrying 112 passengers and a crew made up of three pilots, two stewardesses and a mechanic.
Plane accidents frequently occur in DR Congo which are often blamed on ageing and poorly maintained aircraft, the flouting of safety rules and bad weather.