"The active phase of the operation is continuing. We will not stop," said Arsen Avakov on his Facebook page.
"Overnight, forces participating in the anti-terrorist operation in Kramatorsk took control of the TV tower that was previously held by the terrorists," added the minister.
Kramatorsk lies some 17 kilometres to the south of the flashpoint town of Slavyansk, where the army mounted a major offensive on Friday that claimed at least nine lives, including two servicemen as rebels shot down a pair of army helicopters.
The dawn raid on Kramatorsk comes after Ukraine suffered its bloodiest day since the Western-backed government in Kiev came to power.
In addition to the nine killed in Slavyansk, more than 30 people died in what Avakov called a "criminal" blaze in the southern port city of Odessa following deadly clashes between pro-Russian militants and supporters of national unity.
The authorities in Kiev have admitted the police are "helpless" to contain the pro-Moscow insurgency that has swept through more than a dozen towns and cities in the eastern part of the country.
The Ukrainian government and the West believe that the Kremlin is fomenting the chaos in a bid to destabilise the former Soviet republic ahead of planned May 25 elections.
Moscow denies the charges and has warned that Kiev faces "catastrophic consequences" if it continues what it sees as a military operation against its own people.
Russia has an estimated 40,000 troops on the Ukrainian border and Kiev has reintroduced conscription and put its armed force on full combat alert, fearing an imminent invasion.