The Kiev government, trying to break rebellions by pro-Russia militias which it fears could lead to dismemberment of the country, said more than 300 rebels had been killed in the past 24 hours in the "anti-terrorist operation" centred on the town, a strategically located separatist stronghold.
Rebels denied this and said losses by the Ukrainian side during a government offensive which began on Tuesday exceeded theirs.
At an army checkpoint on the edge of the town, the crash of heavy artillery shelling could be heard and a plume of black smoke rose above the outskirts.
Sustained bursts of automatic gunfire rattled out from leafy areas in nearby fields.
Fleeing the fighting, families came through the barbed wire checkpoint in small groups, taking with them only as much as they could carry.
"It's a mess," Marina, a young woman, sobbed as she clutched her husband's arm.
Balancing his four-year-old daughter on his hip, Andrei Bander, 37, said he feared he would not be back any day soon.
"We took only what was most necessary. We are going. We don't even know where. We will head to Russia though because it's clear we need to leave Ukraine. I don't see anything good left here," he said, waiting for a taxi in the no man's land beyond the check point with only a few small bags.
"In the past few days, from 5.30 in the morning until about 1 p.m., we have been sitting in the basement. We didn't have time to have lunch or wash or anything."
A spokesman for government forces, Vladyslav Seleznyov, said two servicemen had been killed and 45 wounded in "heavy" fighting since the government launched its offensive near Slavyansk, using aircraft, helicopters and artillery.
Separatists, who have controlled the town since early in April, denied the government's casualty figures and claimed to have shot down an army helicopter — something denied by Kiev.
'Reports of 300 dead are not true'
"Reports of 300 dead are not true. Losses to the Ukrainian side were more than ours," Aleksander Boroday, "prime minister" of the self-proclaimed Donetsk People's Republic, was quoted as saying by Interfax news agency.
At a later news conference in the main regional town of Donetsk, Boroday said separatists would mobilize their forces and train volunteers to fight in Slavyansk and "defend" Donetsk.
"We have information that a storming of the city of Donetsk is being prepared by enemy forces and we are being forced to take measures such as mobilization of volunteers," he said.
President-elect Petro Poroshenko ordered the resumption of operations by government forces to quell the rebellion by pro-Russian militia in the Russian-speaking east soon after scoring a resounding victory in an election on May 25.
The pro-Western Poroshenko said on Wednesday in Warsaw where he met U.S. President Barack Obama that he would unveil a plan for a "peaceful resolution" of the situation in the east after his inauguration next Saturday.
Since operations resumed there have been clashes in and around Donetsk and near the border town of Luhansk, with loss of life on both sides.
The Kiev government says the fighting is being stirred up by Moscow, which opposes its pro-Western course.
Kiev also accuses Russia of letting volunteer fighters cross into Ukraine to fight alongside the rebels.
Moscow denies this and renewed calls on Wednesday for Ukraine to end military operations and open dialogue with the separatists.
Though it has only a population of around 130,000 people, Slavyansk has strategic value since it sits at the centre of the Donbass region at the crossroads of eastern Ukraine's three main regions.
Government forces appeared to be significantly tightening their grip on Wednesday but it was too soon to predict the outcome.
In April, initial efforts by the Ukrainian military to root out the separatists flopped with defections and loss of military equipment.
Water in the city has been shut off since Tuesday afternoon, residents fleeing Slavyansk said.
While some families, mainly women and children were trying to leave, some men waited in their cars to get back to the town but were not being let through the roadblock by Ukrainian forces.
Soldiers fired warning shots in the air when one car, coming from the direction of Slavyansk, tried to drive up to the check point.
"My wife and two small children are there, but I can't get back to them," said a resident who gave his name as Sasha, 31.
Just one kilometer (0.62 miles) higher up the road rebels manning their own checkpoint have hung a sheet scrawled with a red-inked warning.
"Those who carry out the orders of the junta are fascists," it read.
"When is [Russian President Vladimir] Putin going to come help us," queried one rebel youth in fatigues and a bandana.
At another separatist road block, a few kilometres away, a volunteer fighter proudly announced he was from the Moscow area.
"This is already war," said another man who said he was from central Ukraine but belonged to a pro-Russian militia group called the Russian Orthodox army.
"This is our land. We will stand here until the last," he said.
The army offensive in Slavyansk followed a daylong firefight on Monday in Luhansk, a town further to the east on the Russian border, after an attack by separatists on a border guard camp.
Government forces acknowledged on Wednesday that a border guard camp in Luhansk had been evacuated and personnel had left with their weapons after an attack by separatists on Monday.
The separatists said the border guards had surrendered.
Zhanna, a resident of a nearby apartment block, said she saw guns and ammunition being removed from the base.
"The [separatist] militia has taken over the building and lowered the Ukrainian flag," she said.
Source: CBC News