The Soviet-era structure is a symbol of Moscow, twice the height of the Eiffel Tower in Paris.
More than 24 hours after the blaze took hold, it was still smouldering in some parts of the structure, but firefighters are reported to have recovered four bodies from a lift high up in the tower.
Russian President Vladimir Putin blamed the fire on the country's economic woes, lamenting the state of its infrastructure.
The fire broke out at 1520 local time (1120 GMT) on Sunday, and at one point spread down to about 100 metres (330ft) above the tower's base.
The blaze is thought to have been caused by an electrical short circuit.
Cables damaged
Minister for Emergencies, Sergei Shoigu, said steel cables that helped to keep the 540m (1772ft) tower vertical had been badly damaged, threatening its stability.
The Soviet-era structure is a symbol of Moscow, twice the height of the Eiffel Tower in Paris.
A rescue official said the heat inside the tower was so intense it had buckled staircases.
The height of the blaze meant it could only be tackled by firemen with hand-held carbon dioxide extinguishers or by helicopters.
The Russian state broadcaster ORT - one of the television channels knocked off the air by the blaze - said on its website that the situation had now "stabilised" and the fire was producing less smoke.
According to Russian Deputy Interior Minister Marat Syrtlanov, quoted by the French news agency AFP, the fire "is now only smouldering".
The fire, which could be seen all over Moscow, forced the main television channels off the air in the capital and also disrupted communications for police and medical services.
The BBC's correspondent Jonathan Charles says it could be weeks before terrestrial broadcasts resume.
Economic woes
Mr Putin, during a meeting with his cabinet, said: "This new accident shows the shape of sensitive installations and the country in general."
"We should not fail to see major problems behind this accident; should not forget the economy," the Interfax news agency quoted him as saying.
"We must fight methodically for economic success."
Exclusion zone
As a precautionary measure, the authorities have established a 700m exclusion zone around the tower, dispersing thousands of people who had gathered to watch the blaze.
The fire broke out about 100 metres above the 340-metre-high viewing platform and restaurant level.
Lifts crashed to the ground as their cables gave way and a huge plume of smoke poured from the upper storeys.
The building is one of Moscow's most popular tourist attractions, but the fire was discovered in time to evacuate visitors down the tower's staircase.
Blank screens
TV stations went off air one by one after the fire broke out, leaving homes without cable TV with blank screens.
State broadcasters RTR and ORT and the main independent station, NTV, resumed broadcasting to most regions by satellite soon afterwards, but Moscow screens remained blank, apart from cable subscribers.
The blaze has turned August into a nightmare month for President Putin and for Russia, the BBC's correspondent Stephen Dalziel says.
First there was a bomb in a Moscow subway, which killed 13 people. Then there was the loss of the nuclear submarine, Kursk, with all 118 of its crew. And the Ostankino tower has long been a source of Russian pride.