Ukrainian government forces have said they re-gained control of the rebel stronghold of Slavyansk.
The defence minister said Ukrainian soldiers hoisted the national flag over the town after pushing most pro-Russia insurgents out.
"A minute ago the Ukrainian national flag was raised over the Slavyansk city council before a line-up of Ukrainian soldiers," said a statement posted on the Ukrainian administration's website, citing Defence Minister Valeriy Geletey.
The town in eastern Ukraine has been at the centre of the fighting between Kiev's troops and the separatists.
Andrei Purgin of the separatist Donetsk People's Republic told The AP news agency that rebels were evacuating, but claimed the army's campaign had left the city "in ruins".
Government forces at a checkpoint near Slavyansk on Friday Ukrainian officials said the offensive was continuing as small groups of rebels were hiding in buildings.
President Petro Poroshenko's website said the separatist fighters had come under mortar fire as they tried to break through government forces' lines.
The website, citing the newly appointed head of the armed forces general staff, said the separatists had lost one tank and other armoured vehicles.
Earlier, a Ukrainian minister had said the rebels and a top commander had fled, though a rebel spokesman said they were relocating to a nearby town.
Slavyansk has been ravaged by heavy fighting The rebels reportedly fled to nearby town of Kramatorsk, but the Reuters news agency said a convoy of about 20 vehicles and buses filled with armed rebels was seen driving out of the town.
If confirmed, regaining control of the area would represent a major success in the government's three-month offensive against the separatists.
Separatists seized the industrial city of nearly 120,000 people on April 6, and on May 30 rebels there brought down a military helicopter killing 14 servicemen.
Ukraine launched its first major assault nearly three months ago This week, Ukraine's ceasefire with pro-Russian separatists expired and Mr Poroshenko said his forces would go on the offensive against the rebels.
But, amid increasing violence, Mr Poroshenko on Friday called for immediate crisis talks with rebel commanders and Russia.
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