The pair are believed to have been visiting the Virunga National Park, a gorilla sanctuary in the east of the African country, when they were abducted on Friday.
A female park ranger travelling with them was killed, according to local media reports.
"We are in close contact with the authorities in Democratic Republic of the Congo following an incident involving two British nationals, and our staff are providing support to their families," a spokesperson for the Foreign Office said.
The park has experienced an increase in violence in recent months.
Armed groups have staged a series of raids to steal resources, particularly charcoal.
Last month, five young rangers and a driver in the park were killed in an ambush.
It was the deadliest attack in recent years and took the total number of rangers killed to 175.
Virunga is a Unesco world heritage site.
It covers 3,000 square miles on the country's border with Uganda and Rwanda.
Founded in 1925, it is home to around a quarter of the world's critically endangered mountain gorillas.