The mayoral race in the Black Sea resort city, set to receive billions of dollars in government funds to prepare for the 2014 Winter Olympics, has attracted unprecedented attention, with several prominent politicians and businessmen campaigning.
The 32-year-old ballerina told reporters: "I feel I have responsibility, strength, and potential. I have not sought approval from the authorities, from the Kremlin, and I will say only one thing: whatever the result of the election, I feel responsible for this city."
She pledged to work to solve the key problems facing the city, including sea pollution and the ageing electricity supply system.
Volochkova is a notorious figure in Russia, appearing regularly in fashion magazines, tabloids and on talk shows. She was famously dismissed from the Bolshoi Theater in 2003, following complaints from her dancing partners that she was "overweight."
The deadline for registering candidates at the city's electoral office is at 18:00 Moscow time today (15:00 GMT).
Other high-profile candidates running for mayor include opposition politician Boris Nemtsov, and tycoon Alexander Lebedev. On Monday, Nemtsov, who was born in Sochi, was attacked with liquid ammonia outside his campaign headquarters by a group of youths that he said were pro-Kremlin activists.
Andrei Lugovoi, the former KGB officer, accused by Britain of murdering dissident Alexander Litvenenko, had earlier planned to run for mayor, but withdrew his candidacy. His party, the ultra-nationalist LDPR, put forward on Thursday Alexei Kolesnikov, a local lawyer, as its candidate.
The official candidate of the pro-Kremlin United Russia Party is Anatoly Pakhomov, currently the city's acting mayor.
