The Kiev government, trying to break rebellions by pro-Russia militias, said over 300 rebels had been killed in the past 24 hours in the "anti-terrorist operation" centred on the eastern town, a strategically located separatist stronghold.
Rebels denied this, saying losses among the Ukrainian forces during an offensive begun on Tuesday exceeded theirs.
At an army checkpoint on the edge of town, heavy artillery shelling could be heard while a plume of black smoke rose above the outskirts. Automatic gunfire rattled out from nearby fields.
Families fled the fighting through a barbed-wire checkpoint with only as much as they could carry. "It's a mess," sobbed a young woman as she clutched her husband's arm. "It's war."
Andrei Bander left with his four-year-old daughter. "We are going. We don't even know where. We will head to Russia though because it's clear we need to leave Ukraine," he said, waiting for a taxi in a small a no-man's land between the two sides.
In support for the Ukrainian forces, acting President Oleksander Turchinov and Interior Minister Arsen Avakov paid an impromptu visit, clad in flak jackets, to another army roadblock on the far side of the encircled town on Wednesday.
A spokesman for government forces said two soldiers had been killed and 45 wounded since Kiev launched its offensive near Slaviansk with aircraft, helicopters and artillery.
Separatists controlling the town since early April denied the government's casualty figures and claimed to have shot down an army helicopter - something denied in turn by Kiev.
"Losses to the Ukrainian side were more than ours," said Aleksander Boroday, "prime minister" of the self-proclaimed Donetsk People's Republic. He said nine had died and 15 were injured among separatists forces in Slaviansk.
At a news conference in the regional capital Donetsk, he said separatists would mobilise forces and train volunteers to fight in Slaviansk and defend their positions in Donetsk.
President-elect Petro Poroshenko ordered the resumption of operations by government forces soon after his May 25 election to quell the rebellion by militia in the Russian-speaking, where people were largely unable or unwilling to vote in the poll.
In Warsaw, where he met U.S. President Barack Obama, he said he would unveil a plan for a "peaceful resolution" of the situation in the east after his inauguration next Saturday.
Kiev says the fighting was stirred up by Moscow, which opposes its pro-Western course, and accuses Russia of letting volunteers cross into Ukraine to fight alongside the rebels.
Moscow denies this and renewed calls on Wednesday for Ukraine to open dialogue with the separatists. But the separatists look to Moscow for help.
"When is (Russian President Vladimir) Putin going to come help us?" asked a young man in fatigues at a rebel checkpoint.
ANTAGONISM TOWARDS KIEV
A few kilometres away, a man from central Ukraine said he belonged to a separatist group called the Russian Orthodox army. "This is our land. We will stand here until the last," he said.
Slaviansk, a separatist stronghold of 130,000, has strategic value since it sits at the centre of the Donbass region at the cross-roads of eastern Ukraine's three main regions.
Government forces appeared to be tightening their grip but it was too soon to predict the outcome. A government camp in Luhansk, further to the east on the Russian border, was evacuated after an attack by separatists on Monday.
The military operation has hardened antagonism against the present government that came to power when President Viktor Yanokovich was toppled in February after mass protests in Kiev.
"Our Ukrainian army is not protecting us, instead it is attacking us. Thanks to them I have to flee my own land," said Larissa Zhuratova, a Slaviansk resident piling onto a bus full of refugees bound for Moscow.
Men were mostly not being let through the army checkpoint.
At a run-down dormitory in a village some 100 km south of the fighting, an eight-year-old refugee mimicked the sound of shelling. "It went ba-boom. We sat in the bathtub," little Vitaly said, playing with toys gifted by local residents.