Ukrainian military and special forces gathered outside Slavyansk on Tuesday in the first real show of force since Kiev announced an "anti-terrorist" operation at the weekend aimed at wresting the city from armed protesters and unmarked soldiers reported to be Russian.

Not long after the Ukrainian operation was launched, Russia's state news agency reported that two pro-Russian insurgents had been wounded in a skirmish near Kramatorsk airport, outside the city of Slavyansk. Heavy gunfire was heard by journalists assembled outside the airport compound. Later the same agency reported that four insurgents had been killed in the clashes - reports that have not been confirmed elsewhere but were referred to by the Russian foreign ministry who said they were "deeply" concerning.

RIA-Novosti reported that the skirmish began when Ukrainian soldiers in an armoured personnel carrier started talking with separatists occupying the site. It did not give any details about who started shooting.

The commander of the anti-terrorist operation, General Vasily Krotov, confirmed to journalists that government forces had seized an airfield in Kramatorsk. As he spoke, four helicopters arrived and flew off loaded with special forces troops.

A large armoured column and special forces moved towards Slavyansk – seven buses filled with 100 paratroopers, 20 tanks and armoured personnel carriers moved within 40 kilometres (25 miles) of the city and set up a checkpoint to control traffic leading to the economically depressed industrial city of 100,000 that has been under effective control of separatist gunmen since Saturday.

"They must be warned that if they do not lay down their arms, they will be destroyed," Krutov said, claiming that the wave of unrest in Ukraine's east was being led by Russian forces. He said more than 300 Russian forces had infiltrated neighbouring Luhansk region on Monday.

"We need to destroy this foreign invader," Krutov said. "We have among these spies Russian military, professionals with long experience in all sorts of conflicts."

Asked if another ultimatum would be given to those who had seized buildings, Krutov said that would be "too humanitarian". He said civilian casualties were possible but his forces would try to "make sure not one innocent person suffers".

"Unfortunately, we face a difficult situation because those realising their plan are hiding behind human shields," he continued, apparently referring to the many pro-Russian locals who have taken part in building takeovers. "Some of them are cynically working toward their own ends, but many are under the influence of propaganda."

Russian channels have painted the new Kiev government as dominated by nationalists who want to crack down on Russian speakers in the east. The Russian prime minister, Dmitry Medvedev, said on Tuesday he hoped Kiev had "enough brains" to prevent a further escalation of the conflict.

"Ukraine is on the brink of civil war and it is scary," he told a news conference after a meeting with his counterparts from Belarus and Kazakhstan.

Tuesday's operation represented Kiev's most forceful response to date to raids in which state buildings in cities across Ukraine's rust-belt have fallen under the control of pro-Russian militants. A much smaller team of special forces entered and later pulled back from Slavyansk after a shootout on Sunday apparently between Russian and Ukrainian soldiers in which one Ukrainian was killed and two wounded.

Government troops have also set up a checkpoint outside the town of Izyum and searched vehicles driving in and out for weapons.

Roads into Slavyansk were dotted with protester checkpoints, at least one with a Russian flag. Another bore a sign reading: "If we don't do it, nobody will."

The Ukrainian president, Oleksandr Turchynov, had given pro-Russian locals in eastern Ukraine until Monday morning to give up their arms and the buildings they had seized, but instead a pro-Russian mob took over yet another government building in Horlivka that day. A man who appointed a new police chief there later said he was a Lieutenant colonel in the Russian army.

The military moves came as western powers stepped up calls for Russia to act to end the crisis in Ukraine. The US president, Barack Obama, told his Russian counterpart, Vladimir Putin, in a tense telephone call on Monday night that Moscow should use its influence to get separatists in the country to stand down. The US has also deployed additional fighter aircraft to the Baltic states and Poland.

The British foreign secretary, William Hague, on Tuesday warned Russia it faced being frozen out by the west for years if it did not stop destabilising Ukraine. The Nato chief, Anders Fogh Rasmussen, joined the US and UK in issuing an urgent public call on Russia to de-escalate tensions in the Ukraine.

Hague said it defied common sense for Putin to deny that the storming of government buildings in eastern Ukraine had been carried out by Russians.

Russia insisted on Tuesday that any sanctions against Moscow over the Ukraine crisis would be counterproductive. "We declare once again that any sanctions against Russia would be groundless and counterproductive," the Russian foreign ministry said in a statement. "Instead of scaring us with another set of sanctions, the European Union should focus on the joint search for a solution for Ukraine's internal crisis."

The mayor of Slavyansk, where pro-Russian armed men have seized police and security service buildings, said on Ukrainian television on Tuesday that troops from Russia and Crimea had been involved in the takeovers.

"Today they actually seized city hall," Nelya Shtepa said on the channel 112 Ukraine. "There are definitely green men there today, they aren't hiding that they're from Crimea, from Russia," she said, referring to the unmarked soldiers Russia deployed to take control of Crimea last month, who are popularly known as "little green men".

Shtepa had initially supported the takeovers on Saturday, walking among the pro-Russian protesters filling the streets in a bright pink jacket and calling the occupiers "our guys".

But on Monday a man who identified himself as Vyacheslav Ponomaryov appeared on the barricades claiming Shtepa had fled, and declaring himself the new mayor. He later made a statement calling on Putin to deploy troops to eastern Ukraine.

Shtepa said she did not know Ponomaryov and had only supported the occupiers because she feared for the safety of policemen who had been taken captive.

After a mob seized police headquarters in Horlivka on Monday, a man in camouflage appointed a new police chief, later identifying himself as a lieutenant colonel in the Russian army.

Pro-Russian protesters, many of them armed, continued to occupy government, police and other administrative buildings in at least nine cities in the country's Russian-speaking east of the country, demanding broader autonomy and closer ties with Russia. The central government has so far been unable to rein in the separatists, and many of the local security forces have switched to their side.

Early on Tuesday, pro-Russian separatists pulled out of one building they had occupied in Kramatorsk but then seized another in the same town, officials said.

Police first said separatists had voluntarily surrendered the police headquarters, though another version issued by police later said they quit the building as a result of negotiations. Later on Tuesday a state security service (SBU) spokeswoman said rebels had occupied the local SBU offices in the same town. She gave no details.

Obama told Putin on Monday that the US preferred a diplomatic solution to the crisis but criticised Russia for taking actions that were not "conducive" to such a path. He said Kiev had made "real offers" to address concerns about the decentralisation of powers to local governments in the country, a senior US government official said.

In a sign of rising tensions, the Pentagon said on Monday that a Russian military fighter flew past a navy destroyer in the Black Sea 12 times over the weekend in a "provocative and unprofessional" move.

The unarmed fighter Su-24 aircraft, or Fencer, made 12 low-altitude passes of the USS Donald Cook on Saturday, coming within 1,000 yards of the vessel, according to the Pentagon. The incident lasted around 90 minutes and a Pentagon source said the USS Donald Cook "was never under threat" and was "more than capable of defending herself".