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.
Soldiers and park rangers are taking part in an operation to find two United Kingdom tourists kidnapped in the Democratic Republic of the Congo.
On its website, it has advised against "all but essential travel" to some Eastern cities amid an increase in reports of attacks by armed groups as well as military and police stop-and-search checkpoints. Virunga National Park has seen more than 170 rangers get killed over the past 20 years as anti-government rebel groups, local bandits and rare animal hunters roam the area.
Mr Mbiye, a father of five, told The Sunday Telegraph last night: "I was driving from Kibumba, heading to the volcano around 9am with a young British couple and a ranger when four heavily armed guys jumped on the road and started shooting in our direction".
The UK Foreign Office said in a statement: "We are in close contact with the authorities in the Democratic Republic of the Congo following an incident involving two British nationals, and our staff are providing support to their families".More news: White House official derides McCain over Haspel opposition: 'He's dying anyway'
There are more species of mammals, birds and reptiles in the park than anywhere else on Earth, and almost a third of the world's 1,000-odd mountain gorillas.
Last year, a fifth of the park's southern sector was deforested owing to illegal charcoal production, the park said.
Rising violence in recent months across the province of North Kivu has been linked to broader political instability in DR Congo. The other location is the Bwindi Impenetrable National Park in Uganda.
The park reportedly witnessed multiple kidnappings over the past two months, attributed to Mai-Mai militia.