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In exchanges marking a sharp escalation in the three-month conflict, jets struck at the "epicentre" of the battle against rebels near the border with Russia, a military spokesman said.
The planes targeted positions from where separatists, using high-powered Grad missiles, bombarded an army motorised brigade on Friday (local time), killing 23 servicemen.
Warplanes also struck at targets near Donetsk, the east's main town where rebels have dug in, destroying a powerful fighter base near Dzerzhinsk, Andriy Lysenko, a spokesman for the "anti-terrorist operation" said.
"According to preliminary assessment, Ukrainian pilots ... killed about 500 (rebel) fighters and damaged two armoured transporters," Lysenko told journalists.
In an earlier air attack on a base near Perevalsk, north of Donetsk, two tanks, 10 armoured vehicles and "about 500" rebel fighters were destroyed, he said.
Rebel representatives, quoted by Russian news agencies, denied they suffered big losses and said the Ukrainians were using outdated intelligence on where separatist forces were deployed.
"There were no volunteers (rebels) where the Ukrainian aviation was active yesterday," said a spokeswoman for the Luhansk-based separatists, referring to the Peravalsk attack.
Earlier, the border guard service said jet fighters were scrambled to strike at the pro-Russian separatists after they resumed missile attacks on government forces deployed near the frontier with Russia, south-east of the city of Luhansk.
In the military action, which began on Friday evening and continued well into Saturday, five Ukrainian servicemen were killed, Lysenko said. There were 16 overflights by Ukrainian fighter jets in all, he said.
The surge in violence on Ukraine's border with Russia, south east of Luhansk which is controlled by separatists, sparked fresh Ukrainian accusations against Russia of involvement in the border fighting.
Ukraine's Foreign Ministry demanded Russia stop supporting armed groups in its eastern region, and end "provocations" on the border.
"The Russian side cynically disregards the fact that Ukrainian servicemen and peaceful civilians are being killed at the hands of terrorists whom it is supporting," the Foreign Ministry said.
"But, on the other hand Russian border guards complained in a letter about Russian household pets being killed by a supposed Ukrainian artillery shell, 500 metres (yards) from the border."
Rebels had also carried out mortar and missile bombardment of army checkpoints at Dyakove and Nyzhnoderevechka near Luhansk, the "anti-terrorist operation" said.
Journalists based in Donetsk said Ukrainian forces shelled Maryinka, a suburb, on Friday night and apartment blocks bore traces of fire on Saturday.
Igor Strelkov, separatist commander in Donetsk, said his men had headed off a plan to move fighters and armour into the area. Subsequent Ukrainian shelling had killed 30 civilians and the number of casualties could rise, he said.
Vladyslav Seleznyov, main spokesman for the "anti-terrorist operation", said the violence there had been caused by rebels out to discredit the Ukrainian armed forces.
Poroshenko, whose forces recently seemed to be prevailing over the rebels, vowed on Friday to "find and destroy" rebels responsible for the missile attack at Zelenopillya, which also wounded nearly 100 and was one of the deadliest yet against government forces.
NEW SENSE OF URGENCY
The increasing violence will bring a new sense of urgency to diplomatic attempts to end the worst crisis between Russia and the West since the Cold War.
After a pro-Western revolt in Kiev ousted a Moscow-backed president in February, Russia annexed Ukraine's Crimean peninsula and pro-Russian separatists seized strategic buildings in towns in the Russian-speaking east, setting up "people's republics" and declaring they wanted to join Russia.
More than 200 Ukrainian servicemen have been killed since then, and hundreds of civilians and rebels have also died.
The United States and the European Union have brought in limited sanctions against Russian businesses amid Ukrainian allegations that Moscow has fanned the conflict and turned a blind eye to military equipment and Russian fighters crossing the border.
On Saturday, the EU targeted 11 Ukrainian separatist leaders with travel bans and asset freezes, swerving away from fresh sanctions on Russian business to avoid antagonising its main energy supplier.
The rebels' missile strike on Friday at a motorised brigade was against part of a contingent of troops sent to the area specifically to try to block military equipment and guns being brought in from Russia to help the rebels.
Rebel fighters said Ukrainian fighter planes had also carried out air strikes on Saturday in the eastern town of Horlivka. "There were a series of powerful explosions. Details are being clarified," a separatist representative, Konstantin Knyrik, was quoted as saying by Russia's Interfax news agency.
EYES ON CONTACT GROUP
Friday's military setback at Zelenopillya took the gloss off the government's recapture of the rebel stronghold of Slaviansk last weekend.
The Ukrainian military, following the Slaviansk victory, says it has readied a plan to oust the rebels now from Donetsk, a city of 900,000 people where separatist forces are dug in.
Poroshenko has said the military plan will be aimed at protecting civilians there and had appeared to rule out the use of air strikes and artillery to crush the rebels.
Poroshenko, who was also urged by German Chancellor Angela Merkel to use a sense of proportion in actions against the separatists, had further talks on Friday with Donetsk mayor Aleksander Lukyanchenko on the issue.
Western allies and Russia are pressing for a new meeting of the 'contact group' involving separatist leaders to try to negotiate an end to the crisis.
Poroshenko says he has proposed various venues for the talks but has said there will be no repeat of a 10-day unilateral ceasefire by government forces which lapsed on June 30.
The Ukrainian government says that ceasefire was repeatedly violated by the rebels and that more than 20 Ukrainian servicemen were killed while it was in force.