Soldiers and volunteers have been racing to reinforce dykes and other protective barriers, but the water level has already crept above the critical level and some outlying districts are flooded.
Supersonic jets are continuing to bomb ice-jams downriver in the hope of reducing water levels.
Yakutsk is the capital of the Yakutia region which is suffering Russia's worst floods in 100 years.
Thousands of people have been evacuated from the suburbs of Yakutsk to the city centre, several metres higher than the flood mark.
But others have refused to leave, staying perched on their roofs surrounded by water, saying they feared looters.
One elderly woman chained herself to her bed to resist evacuation, but was removed by helicopter along with her bed, according to Russian television.
Levels rising
Emergencies Ministry sources told ITAR-TASS news agency that the dykes could break apart at any moment.
Water levels had already reached 8.34 metres by 1600 local time (0600 GMT) and were rising by several centimetres an hour. Even with present emergency measures, the city can currently only withstand levels of up to 9.5 metres.
Though spring flooding is an annual occurrence in Russia, the current exceptional levels could devastate Yakutsk.
It is built on concrete stilts, driven into the permafrost by steam hammers.
Before the floods, scientists predicted that the thaw of the permafrost resulting from climate change could destroy most of the city's buildings by 2030.
Fatality
The severe spring flooding has left almost 5,000 homes under water in 32 towns and villages from the Volga river in European Russia to the Far East.
There has been one fatality. In Lensk, a 70-year-old woman drowned when she and her husband tried to escape in a boat.
Some 2,000 people have been left homeless in Lensk, and the Russian news agency Itar-Tass quoted the head of the local government, Vasily Vlasov, as saying that the town would probably have to be rebuilt elsewhere, such was the scale of the devastation.
There were warnings earlier this year that Siberia and the Russian Far East could be affected by floods, following one of the harshest winters on record, when temperatures plunged to -50 Celsius.