The Kiev government has said it will act quickly to seize back more territory from rebels after re-taking Slaviansk in what President Petro Poroshenko called a turning point in the three-month conflict against pro-Russian fighters in the east.
Rebels retreating from Slaviansk, some driving armoured vehicles flying Russian flags, poured into Donetsk, 65 miles to the north over the weekend before 1,000 of them held a rally in the central square.
Their commander, a Muscovite using the name Igor Strelkov, said his men would fight for the city, which was "much easier to defend than little Slaviansk".
Businesses have closed down and thousands of residents are believed to have fled Donetsk.
The city is the headquarters for Rinat Akhmetov, Ukraine's wealthiest man by far, whose fortune, founded on coal and steel, is put at more than £8 billion by Forbes.
He said government forces should show restraint in Donetsk and the surrounding Donbass region.
Mr Akhmetov added: "Donetsk must not be bombed. Donbass must not be bombed. Cities, towns and infrastructure must not be destroyed. We must avoid suffering and deaths of peaceful people."
The Defence Ministry said separatists had launched 10 attacks on government posts and army positions in the previous 24 hours.