SLAVYANSK, Ukraine - Ukraine’s military suffered heavy casualties in a stepped-up offensive on pro-Russian rebels on Monday, as Europe and the head of the UN made a last-ditch diplomatic effort to reel the country back from the brink of civil war.

At least four Ukrainian servicemen were killed and 30 injured battling heavily armed insurgents around the flashpoint eastern town of Slavyansk as Russia warned the violence was putting peace in Europe in peril.

Russia on Monday warned that towns in eastern Ukraine encircled by Ukrainian troops were facing a humanitarian disaster due to shortages of medicines and food.

“A humanitarian disaster is brewing in the encircled towns - there is already a lack of medicines and there are starting to be disruptions of food supplies,” the Russian foreign ministry said in a statement. The interior ministry in Kiev said the pro-Russian gunmen controlling the town were using civilians as human shields and were shooting from houses, some of which were on fire.

“They are waging a war on us, on our own territory ... my mission is to eliminate the terrorists,” Interior Minister Arsen Avakov told reporters from near Slavyansk where he was overseeing the assault.

The head of Ukraine’s national guard, Stepan Poltorak, said: “We have bottled them up in the centre” of Slavyansk, but added that “our adversaries are well-trained and well-equipped”.

The advance on Slavyansk was part of a wider military operation in the east to root out the separatist insurgents, who are holding more than a dozen towns.

The authorities retook control of the TV tower near Slavyansk but lost a helicopter, cut down by machine gun fire. The pilots survived.

Russia, which denies any hand in the violence, warned in a foreign ministry report on Monday that the unrest in Ukraine was now “fraught with such destructive consequences for Europe’s peace, stability and democratic development that it is absolutely necessary to prevent it”.

The report accused Ukrainian “ultra-nationalists” - who Moscow claims control Kiev’s government - of rights violations on a “mass” scale.

But Ukraine’s interim president declared that it was Russian meddling that had brought war to his country. He warned that pro-Russian provocateurs might stage violence in Kiev during celebrations on Friday marking the Soviet victory over Nazi Germany in World War II. “War is in effect being waged against us, and we must be ready to repel this aggression,” said Oleksandr Turchynov, who has placed Ukraine’s armed forces on combat alert and reintroduced conscription amid fears of a Russian invasion.

There were concerns also for the south of Ukraine, in the port city of Odessa, which was seething after a deadly clashes and a fire on Friday that killed 42 people. After an angry pro-Russian crowd on Sunday stormed Odessa’s police headquarters and forced officers inside to free 67 of their arrested fellow activists, authorities moved the 42 remaining inmates to other parts of Ukraine.

Visiting Odessa on Sunday, Prime Minister Arseniy Yatsenyuk vowed a full investigation into the scenes that occurred there last week and blamed what he called the “inefficient” police force.

The unrest was part of a Russian plot “to destroy Ukraine and its statehood,” Yatsenyuk charged.

As diplomats scrambled to dial down the tensions in the worst East-West crisis since the end of the Cold War, UN Secretary General Ban Ki-moon offered to mediate personally between the opposing sides.

Speaking exclusively to AFP in Abu Dhabi, Ban offered “to provide my own role if necessary” before the crisis “spins out of control and creates huge consequences beyond anybody’s control”.

The offer came as European leaders, fearing all-out civil war on their eastern flank, launched a desperate new peace bid, urging Ukraine and Russia to forge a negotiated solution.

The chairman of the Organisation for Security and Cooperation in Europe, Didier Burkhalter, was due in Moscow on Wednesday amid calls for his group to mediate between Kiev and eastern separatists.

The trip by Burkhalter, who is also the Swiss president, was agreed in a phone call between Russian President Vladimir Putin and German Chancellor Angela Merkel late Sunday.

“Putin and Merkel stressed the importance of effective international action - especially by the OSCE - in reducing the tensions in Ukraine,” Russia said in a statement.

Merkel’s office said “round-table discussions” would be set up under OSCE auspices to “facilitate national dialogue before the presidential election” planned for May 25.

German Foreign Minister Frank-Walter Steinmeier said he was in talks with Russia, the United States, the European Union and the OSCE to hold a second peace conference in Geneva.

A first agreement aimed at defusing the crisis was signed in the Swiss city on April 17. But Russia last week pronounced the accord dead after Kiev stepped up military operations that Moscow described as “war against its own people”.

With the rhetoric and fighting heating up, Moscow has described plans to hold the presidential election as “absurd”.

The Kremlin’s stance raises the prospect of tougher US sanctions on whole sectors of the recession-hit Russian economy.

US President Barack Obama has warned the West would step up its punitive action if Moscow continued what he called the “destabilisation” of Ukraine.

French Foreign Minister Laurent Fabius tweeted that Europe was “not responding as it should” to the crisis “because of its energy dependence” on Russia.

Moscow has threatened to turn off the gas taps to Ukraine - and by extension several European countries - if Kiev does not pre-pay its June bill.

The separatists in Ukraine are preparing their own spoiler of the May 25 election with plans to hold an independence referendum on Sunday.

The presidential vote was called by Ukraine’s new leaders shortly after the ouster of pro-Kremlin president Viktor Yanukovych in February, the culmination of months of sometimes deadly pro-EU protests.

French President Francois Hollande stressed that “nothing must hinder” the holding of the poll that US Vice-President Joe Biden has dubbed “maybe the most important election in Ukrainian history”.