The first quake, with a magnitude of 6 and its epicentre in the DRC, happened at 10.30am local time (07:30 GMT), followed by a magnitude 5 quake in densely populated southern Rwanda at 1.56pm.
In Rwanda, 34 people were killed and 231 wounded, according to a health ministry hotline.
Frank Mugambage, an official in the president's office, said several people were killed when their church collapsed.
Mary Gahonzire, Rwanda's deputy police chief, said rescue efforts were under way.
Across the border in the lakeside Congolese city of Bukavu, Raisi Kunda, the mayor, said five people were killed and 149 injured.
Kunda said many homes, as well as schools and churches, were damaged in the city, but the extent was not immediately clear.
"We are monitoring what's going on. We have a special group [beside's the wounded] - people who have been traumatised, it's a big number," ambassador Joseph Mutaboba, at Rwanda's ministry of internal security, told Al Jazeera.
'Church collapsed'
In Rwanda, at least 10 people out of the 34 killed died when a church collapsed in the Rusizi district of Western Province, Radio Rwanda reported.
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Tremors were felt in the Rwandan capital,
Kigali, more than 200km away |
More than a dozen others were killed in Rusizi and Nyamesheke districts and some 250 wounded were transported to various regional hospitals, the radio said.
Tremors from the earthquake were felt in Kigali, the Rwandan capital, over 200km away.
In the DRC, Bernard Watunakanza, the acting governor of Congo's South Kivu province, said that aftershocks were happening "every 20 or 30 minutes".
"Up to now there are five dead and 149 seriously injured. Many people are traumatised," he said.
Reports on Rwandan television said that dozens of people in Bukavu, in the DRC, had died in the earthquake.
Earthquakes are common in the western Great Rift Valley, a seismically active fault line straddling western Uganda, eastern Democratic Republic of Congo, Rwanda and neighbouring Tanzania.