Russia has began major military exercises involving more than 100 aircraft near the border with Ukraine.

The war games on Monday came as the conflict intensified around Donetsk, a city of a million people held by the pro-Russian rebels who have been fighting Kiev government forces since April. Heavy artillery fire continued there on Sunday night, according to the city administration. Ukraine's national security council said on Monday that government troops had begun "liberating Donetsk from the north after encircling the city".

The headquarters of Kiev's "anti-terrorist operation" said rebels had intensified artillery fire at its positions overnight. Both sides have reportedly fired low-accuracy artillery such as Grad rockets in populated areas during the conflict, in which at least 500 civilians have been killed.

A map published by the national security council showed government forces had made significant gains, cutting the rebels in Donetsk off from those in Lugansk. Ukrainian troops had taken back three-quarters of the territory formerly controlled by the rebels, the council said.

Ukraine's defence minister, Valery Geletei, claimed on Monday that Kiev would "be victorious very soon". Andrei Lysenko, a national security council spokesman, said the rebels would be defeated before the onset of winter.

The council also said that artillery based in Russia had fired on Ukrainian soldiers and border guards overnight. It was the latest in a string of claims by Ukraine and Russia accusing each other of cross-border fire.

The Russian military exercises that began on Monday are scheduled to last until Friday and include Su-24, Su-27 and MiG-31 fighter jets, Mi-8, Mi-24 and Mi-28N helicopters, and the recently deployed Su-34 bomber. As part of the exercises, aircraft were to shoot at ground and air-based targets at newly opened testing grounds near Ukraine's south-east border, while air defence forces were to fire surface-to-air missiles near Astrakhan next to the Caspian Sea, the defence ministry said in a statement.

Fighter jets and bombers were also to practice mid-air refuelling from an Il-78 tanker plane above the Arctic Circle.

Last Friday, the Pentagon said 10,000 Russian troops stationed near Ukraine had moved to within 30 miles of the border and continued to build their military capabilities. Russia denied previous US claims of a troop buildup along the border last month, arguing that international monitors had not revealed any violations or undeclared military activities near Ukraine.

Russian and Ukrainian authorities offered differing explanations of how 438 Ukrainian soldiers and border guards wound up on the Russian side of the border overnight. Russia's federal security service said the troops had destroyed their weapons and asked for asylum.

Ukraine's national security council admitted that some troops had retreated into Russian territory during an operation to free a unit surrounded by rebel forces, but said they were forced to retreat to the border after running out of ammunition.