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.
The Britons were among a group of people taken hostage, according to a spokesperson for the Congolese Institute for Nature Conservation (ICCN).
A female park ranger travelling with them was killed and their driver was also abducted, a park spokesman said.
Their vehicle was ambushed while bringing the tourists from Kibumba to the city of Goma, Joel Wengamulay, ICCN spokesman told the UN-backed Radio Okapi.
“For the moment the (ICCN) cannot communicate much about the incident because the hostages are still in captivity. That would put their lives in danger,” he said, adding that investigations have begun into the attack.
“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 about a quarter of the world’s critically endangered mountain gorillas.
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Other endangered species such as lions, elephants, hippos and a number of rare bird species are also located in the park.
Last year, a fifth of the park’s southern sector was deforested owing to illegal charcoal production.