Two strong earthquakes have rocked Rwanda and the Democratic Republic of Congo, killing at least 40 people including 10 who died when a church collapsed.

Nearly 400 people were seriously injured in the two countries after the quakes hit within three hours of each other along the western Great Rift Valley fault.

The first hit eastern Congo at 7.30am with a magnitude of six. A second smaller magnitude five quake struck the nearby southwest of neighbouring Rwanda at 10.56am.

"It was a fear that I cannot even explain. We thought we were already dead," Jacqueline Hachez, who lives in the Congolese town of Bukavu, told Reuters.

Rescuers continued the search for survivors but the authorities fear people who are trapped may die before they can be freed.

Many houses collapsed, cracks appeared in buildings and aftershocks were being felt in Bukavu '"every 20 to 30 minutes".