Dmitry Medvedev, the Russian president, expressed condolences over the blast, saying the country's Black Sea fleet was ready to assist in a rescue operation.
A spokesman for the regional emergency situations ministry said that 21 people had been rescued from the rubble so far.
Two sections of the apartment building, constructed in 1965 and containing about 35 flats, were destroyed in the explosion.
Tymoshenko said that the accident was caused by an explosion of oxygen or acetylene cylinders in the building's basement.
"According to preliminary expert conclusions, there was a workshop in the building's basement where explosive materials have been used without any kind of permission," she said.
Earlier, authorities refused to confirm that it was a gas explosion, the usual explanation for such incidents in apartment buildings in the former Soviet Union.
Witnesses said that the cries of those trapped under the rubble could still be heard overnight, giving rise to hopes that more survivors could be found.
In October 2007, 15 people were killed in a gas explosion that partially destroyed a nine-storey building in Ukraine's eastern city of Dnipropetrovsk.