Two days of chaos and violence in east and south-east Ukraine appeared on Saturday to be pushing the country ever closer to civil war, as the death toll rose to 42 following a military counter-offensive launched by authorities in Kiev against pro-Russia rebels.

An angry crowd confronted police outside the trade union building in Odessa where dozens of pro-Russia activists died on Friday night in a blaze started during clashes with pro-Ukraine protesters. Fighting continued in the east as the Ukrainian army continued to oust pro-Russia rebels.

The region has been rocked by unrest since the new government in Kiev came to power following demonstrations that ousted pro-Russia president Viktor Yanukovych at the end of February. Many in Ukraine's east, which has strong economic and cultural ties with Russia, say they now feel marginalised. What began as small-scale unrest rapidly escalated into an armed rebellion as pro-Russia militia groups seized government buildings. Kiev and its western allies have accused the Kremlin of orchestrating the chaos, which follows a Putin-backed putsch that resulted in Crimea's annexation last month.

Slavyansk was quickly established as the heartland of the pro-Russia forces operating in the region. Armed men, led by self-appointed mayor Vyacheslav Ponomaryov, have controlled the city, ringed by militia-controlled road blockades, for more than two weeks.

In Donetsk, Luhansk, Kostinovka and Horlivka, rebels have seized most of the state security and administrative buildings. Kidnappings and murders have become common as law enforcement officials defect to the rebels.

As the Ukrainian army edged ever closer to the rebel HQ in Slavyansk on Friday, gunfire echoed as fighting raged in the areas surrounding the city. Ambulances tore down the deserted streets throughout the night to collect the wounded and dead.

Local people claim the Ukrainian army shot at unarmed citizens who formed a human chain near a road blockade on the edge of the village of Andreevka, only a few miles from Slavyansk. "They are killing peaceful people," said Igor, 29, a farmworker from the village who was receiving treatment at the Slavyansk hospital for a shrapnel injury he said he suffered during the night assault.

"I'm just a local citizen, unarmed. People ran away when they started shooting at us," he said. Those with more serious injuries were reportedly taken to the nearby Kramatorsk hospital. Some suggest that ambulances and cars carrying the dead and wounded were not allowed to pass by the Ukrainian military.

The total number of rebel losses cannot be confirmed, but a spokeswoman for Ponomaryov said that at least 10 militia and 30 civilians had died. "Countless more are injured," she said, "and the number is growing every second."

Less than 24 hours after the counter-terrorism assault against the rebels began, Ponomaryov announced the release of seven Organisation for Security and Co-operation in Europe (OSCE) officials and their civilian translator, who were taken by bus to Donetsk. Some have interpreted the move as a bid by the Russia-backed rebels to reduce tensions. The mayor's spokeswoman said the "guests" had left "without conditions".

After a brief hiatus, fighting resumed around midday on Saturday as the Ukrainian army advanced in Kramatorsk. In an attempt to counter the attack, lorries and buses were used to fortify the barricades and block Ukrainian armoured personnel carriers from entering the city by road.

Local militia set tyre barricades ablaze in a bid to create a thick screen of black smoke to hold back the Ukrainian advance. Both sides shot at each other intermittently for several hours.

One Ukrainian soldier stationed at a checkpoint in Kramatorsk said he had come under heavy fire and expected resistance by the rebels to continue through the night.

The Kiev counter-terrorism operation is the first real attempt to dislodge the rebels from their stronghold. Two previous bids to oust the rebels ended almost as soon as they had begun when Ukrainian army units leading the operation either surrendered to the militia or were captured almost immediately. Strong local support for the rebel movement has proved a major barrier to Kiev in responding to the situation and the spate of violence.

Many in Slavyansk see the Ukrainian army as an invading rather than liberating force. "I understand the soldiers; they have signed up and now they don't know what to do," said market-stall owner Tatiana, 50. "The government are pitching people here against each other."

Behind her, a homemade banner taped to a statue of Lenin outside the rebel headquarters in the city's administration building summed up local sentiment about the anti-terrorism operation: "Turchynov and Yatsenyuk [Ukraine's interim president and prime minister] are killers".

At the foot of the monument, local people have started placing flowers in memory of the latest round of those killed. "I'm sorry we couldn't protect you," sobbed one pensioner on her husband's shoulder as she came to pay her respects at the memorial. The fighting and increased isolation in the east – television stations have been turned on and off by the opposing forces – have proved a fertile breeding ground for Russia's churning propaganda machine, which has played a central role in fuelling the conflict.

Many believe that foreign forces and nationalist groups are acting as part of the Kiev-led operation under the auspices of the Ukrainian army. "They are here: the US army, mercenaries, Right Sector," sobbed 48-year-old Yelena in the city's central square. "You see what they have done in Odessa. They want to kill us, to destroy us totally."

Ponomaryov, who yesterday celebrated his birthday as Ukrainian forces advanced on the city, has called on Russia to deliver the promised reinforcements now that they are under attack by Ukrainian forces. But so far the Kremlin has not responded, other than to say that Moscow has "lost control" over the rebels operating in Ukraine's east.

"Where is Russia? Putin stays silent. Russia, Russia, there is no Russia here. Why? We beg Putin to come and save us," said Yelena, visibly distraught. She drew a comparison between the situation in Ukraine's east and the wars that ravaged the Balkans in the 1990s, adding that she would like to evacuate her children from the city but that people are unable to leave.

A double tier of barricades now surrounds Slavyansk. In some places pro-Russia militia checkpoints are separated from the Ukrainian army by only a few miles of tarmac. A gauntlet of tree trunks, felled by local people sympathetic to the rebels, blocks the main routes in and out of the city, making access by vehicle almost impossible. Handfuls of people are making their way out by foot to surrounding villages. "I would rip the Ukrainian army apart with my teeth if I could" said 35-year-old builder Vasily as he stood guard with a group of others at his village's main road leading toward Slavyansk.

Just two days ago, the advancing Ukrainian army passed through the village, fuelling anger in the local population. "We don't want them here. Who invited them? Why are they attacking peaceful people?" he asked.

But as Kiev made advances in one front, losses occurred on the other. As evening fell on Saturday around 100 unarmed men wearing ragtag military fatigues stormed the security force building in Donetsk, meeting minimal resistance from the local police who watched from a distance. Security forces across the region have defected to the militia's side, and the easy capture followed a pattern of seizures in the region that appear to have been prearranged with police chiefs.

The rebels looted the building before turning their attentions to the nearby private office of the governor of Donetsk, Sergey Taruta. The rebels seized Taruta's state office, located on the city's administrative building's 11th floor, nearly a month ago. Since then local government has been operating out of a hotel in the city centre.