Ukraine's mines are among the most dangerous in the world
They say more than 60 other miners were injured in the accident at the Zasiadko mine in Donetsk.
Ukraine's emergencies ministry said "an unexpected eruption of a coal and gas mixture" happened at a depth of more than 1,000m (3,300ft) underground.
Ukraine had some of the world's most dangerous mines, many of which date to Soviet times.
The sector is considered to be under-funded and have poor safety standards.
The accident happened at about 0510 local time (0210 GMT) on Wednesday morning, Ukraine's emergencies ministry spokesman Ihor Krol said.
The bodies of 13 miners were found by rescue teams, officials said. Many of the injured were taken to hospital.
About 400 miners were working in the mine at the time of the blast. Most of them have been evacuated and work halted.
Ukrainian officials said that the rescue operation was now over.
They also denied earlier media reports that a blast was the cause of the accident.
The Zasiadko mine - one of Ukraine's biggest - has a reputation as one of the most deadly.
In 2002, a methane blast killed 20 miners there. A similar explosion a year earlier left more than 50 miners dead.
In 1999, 50 people were killed in a blast at the mine.
More than 4,000 miners have been killed in accidents since Ukraine became independent in 1991.
Co najmniej 32 górników zginęło podczas eksplozji w kopalni w Kazachstanie, 8 uznaje się za zaginionych. Przyczyną wybuchu był prawdopodobnie wyciek metanu. Pozostałym 300 górnikom pracującym w chwili wybuchu udało się wydostać na powierzchnię.

Również na Ukrainie doszło do wybuchu w kopalni „Zasiadko” w Doniecku. Zginęło 13 górników, a wielu jest rannych. Również tutaj przyczyną eksplozji, do której doszło na głębokości 1000m jest prawdopodobnie wyciek metanu. W ukraińskich kopalniach zginęło ponad 4000 górników od 1991 r.