The capercaillie is a native species that became extinct in Britain in the mid-18th Century but were reintroduced in Perthshire in 1837.
Earlier this year the Scottish government announced an emergency plan to boost numbers in the Cairngorms.
Breeding male capercaillies have increased by by 50% since 2020, but numbers had declined as a result of habitat loss, eggs being eaten and the birds flying into deer fences.
Ospreys are migratory birds and some fly more than 3,000 miles (4,828km) from west Africa to breed in Scotland.
In 1954, Loch Garten had the first confirmed pair of breeding ospreys since the species went extinct in the UK in 1916 due to habitat loss and persecution.
Ross Ewing, from Scottish Land and Estates, said the incident was “clearly serious and fast-moving” and urged members of the public to keep routes clear for emergency vehicles.
He also encouraged landowners and land managers to take precautionary measures including the readying of specialist fire equipment.
Staff at Glenmore Outdoor Centre, which is near the blaze, asked people not to travel to the area.
They said: “Follow official advice from Scottish Fire and Rescue Service, and be patient with staff while the ongoing situation is managed appropriately.”
A spokesperson for the Cairngorms National Park Authority said the fire was “deeply concerning”.
They added: “This incident – alongside wildfires we are seeing across the UK this week – serves as a stark reminder of the risks that periods of drier, hotter weather can pose.”