Ukraine's president, Petro Poroshenko, has claimed that serving Russian military officers are taking part in operations in east Ukraine, after an An-26 transport plane was reportedly shot down near the border.

A statement on the president's website said the aircraft was flying at an altitude high enough to evade any of the weapons that separatists were known to have, and was "probably" attacked from inside Russian territory.

It was not immediately clear how many military personnel were on board the plane, but there were reports that some had managed to parachute to safety and make contact with military HQ in Kiev.

After a lull when all sides appeared to be seeking a way out of the conflict, tension has risen again in recent days as Ukrainian troops have moved to retake towns held by the rebels, and separatist fighters have regrouped in the regional centres of Donetsk and Luhansk.

Russian politicians have demanded targeted strikes on Ukrainian territory after a shell apparently fired by pro-Kiev forces landed in a residential area on the Russian side of the border, killing one person. Russia's foreign ministry warned that the shelling could have "irreversible consequences", while the Ukrainians have been sounding the alarm over what they claim is more overt Russian involvement than ever before.

President Vladimir Putin's spokesperson Dmitry Peskov said rumours of a Russian ground invasion in the next 24 hours were "nonsense".

On Sunday night, Ukrainian forces launched a fresh offensive on the outskirts of Luhansk in an attempt to reach government troops besieged by rebels for more than a month at the city's airport.

Both sides fired heavy artillery in a fierce fight to the south-east of the city, pausing briefly during the World Cup final, only to resume fire again until the early hours of the morning. The Ukrainian army claimed it had broken the blockade of the airport.

Air strikes and mortar fire also hit the outskirts of the city. Pro-Russia gunmen manning the final rebel checkpoint to the south-west of Luhansk said they had come under heavy assault during the night.

A spokesperson for the Luhansk People's Republic – one of two separatist enclaves set up after referendums in May – said several civilians were injured and three killed.

The Ukrainian forces also suffered losses. On a bridge near the airport on Monday afternoon, armed rebels ransacked a burnt-out government truck and armoured personnel carrier for salvageable weapons.

The vehicles – travelling in a convoy of 10 – had been caught an ambush as they approached the airport during the night. Unexploded ammunition littered the tarmac; on the grass beyond the road barrier lay the bodies of two Ukrainian soldiers.

At their camp in the woods nearby, rebel fighters said they had also lost two men in the skirmish. "We will kill them here and they we will go to Kiev, we will chase them all the way to America," Alexy, one of the gunmen, told the Guardian.

As fighting continues around the last separatist strongholds, Ukrainian authorities are asserting their presence in the towns they have retaken. Dozens of troops and police patrolled the streets of Siversk, a town of 10,000 that was taken by government troops on Thursday after a two-day fight.

Inside the city hall, Captain Valery Levchenko, 39, said government intelligence agencies had mapped the main separatist positions in the town, which were then targeted with artillery and air strikes before troops launched a ground attack.

Police were now attempting to restore public order while sappers cleared landmines. Levchenko claimed that civilians were mostly pleased to see the troops. A local official who asked not to be named said one woman was killed and her husband lost both his legs in the bombardment. About 70% of the population had already left the town to escape the fighting, he added.

Tamara Yarontseva, 50, said she was happy to see the government soldiers in Siversk. Her family had fled their home, which was near a major rebel base, after a shell destroyed the kitchen.

"Then we moved to the suburbs, hoping we would be safe, but we also spent a lot of time hiding in the cellar," she said. Yarontseva said that when the separatists arrived in early May many locals supported them, assuming that Russian troops would soon arrive and annex the territory, as happened in Crimea. Soon, however, support turned to mistrust as the rebels stole cars and other property, she said.

Separatist fighters are still hiding out in the woods outside of Siversk, shooting at army checkpoints every night, according to the government troops, who said they planned to retake Donetsk and Luhansk in the same way they captured Siversk.

"The negotiations make no sense any more," Levchenko said. "So many people died already on both sides. They hate us and we hate them. It's war."

Russian officials have somewhat toned down rhetoric over Ukraine in recent weeks, but state-controlled television is still taking a hard line and frequently compares events in Ukraine to those in Nazi Germany.

Particular controversy was caused over the weekend when Channel One aired a report claiming that the Ukrainian army had crucified a three-year-old boy in the central square of Slavyansk, a rebel stronghold recaptured by Ukrainian forces.

"They gathered women on the square because there are no more men. Women, girls, old people," said a woman named as Galina Pyshnyak, apparently a refugee from Slavyansk. "They took a child of around three years old, a little boy in his underwear and a T-shirt and nailed him to a noticeboard like Jesus. One was nailing him and two others holding him."

No other news organisations have found evidence of such an event, and a spokeswoman for Ukraine's interior ministry told AFP that the report was "following in the footsteps of Goebbels".