As a Russian humanitarian convoy arrived at the border accompanied by military vehicles, Kiev's forces continued their grinding advance against separatists strongholds in the Donetsk and Luhansk regions.
Two rebel commanders resigned on Thursday, continuing the departure of the movement's leadership in the face of Ukrainian gains.
Statements from the Ukrainian military on Friday suggested the conflict was entering its endgame but that victory would not come immediately.
"We have done the preparatory work for the final stage, the liberation of cities. I should say it will take more than one or two days," military spokesman Colonel Andriy Lysenko said on Friday.
He said government forces had completely surrounded Luhansk and were retaking the city "step-by-step" from rebels equipped with armour and artillery.
Residents of the city have been without water, electricity and mobile phone services for over a week.
A spokesman for Kiev's "anti-terrorist operation" said in a video statement on Friday that its forces had retaken three towns in eastern Ukraine.
The national security council said nine soldiers had been killed and 18 wounded on Thursday and Friday.
But pro-Russian sources told a much different story.
Pro-Russian Twitter accounts were claiming a wide-ranging rebel counterattack in Pervomaisk and other towns.
Meanwhile the Russian president, Vladimir Putin, whose country has provided the rebels with volunteers, supplies and weapons, promised to do everything possible to end the bloodshed in eastern Ukraine in a conciliatory speech on Thursday in the recently annexed territory of Crimea.
"We need to consolidate and mobilise but not for war or any kind of confrontation … for hard work in the name of Russia," he said.
According to local authorities, artillery fire and explosions could be heard on Friday afternoon in the centre of Donetsk, the city that Kiev has said will be the site of the final battle with the rebels.
Eleven residents were killed and eight wounded after intensive shelling of the city centre on Thursday and fighting in outlying regions overnight, city hall said.
Incendiary bombs were reported overnight and electricity had been cut off to the Leninsky district of the city.
The death toll in the eastern Ukraine conflict nearly doubled between 26 July and 10 August, the United Nations human rights office said on Wednesday, rising from 1,129 to 2,086 as government forces redoubled efforts to reconquer rebel territory.
A rebel Twitter account reported on Friday that the Aidar battalion, one of the recently organised volunteer groups that have contributed thousands of fighters to Kiev's campaign, had suffered 22 killed and 36 wounded in fighting on the road between Luhansk and the Russian border.
Lysenko said he wasn't sure exactly how many men the battalion had lost but denied it had suffered such heavy casualties.
The resignation of top pro-Russia leaders suggested the rebellion was beginning to come apart, or that Moscow was deliberately withdrawing its commanders from the conflict.
The top rebel military leader, Igor Strelkov, who has admitted to serving in Russia's intelligence services, stepped down on Thursday to take a new job, rebel sources reported.
The news followed reports that Strelkov had been seriously injured in the fighting, although his representatives later denied this.
The same day, Valery Bolotov resigned as head of the self-declared Luhansk People's Republic, saying that an injury was preventing him from carrying out his duties.
Alexander Borodai, a Russian political consultant and friend of Strelkov, had resigned last Thursday as head of the self-declared Donetsk People's Republic and returned to Moscow.
In this manner, the rebels in both regions had lost their most senior leaders in the space of one week.
A map of the conflict zone published by the national security council on Friday showed that government forces were attacking Makeyevka, a city just outside of Donetsk, and advancing toward the rebel-controlled border with Russia in the Luhansk region.
According to the map, the troops had completely surrounded the city of Luhansk and retained control of a thin strip of territory cutting the rebels in the Luhansk region off from their counterparts in and around Donetsk.
However, other pro-Ukrainian observers claimed this and other maps were too optimistic about Kiev's progress.
Dmitry Tymchuk, a defence analyst with close ties to the government, said rebel forces were counter-attacking in several areas and attempting to retake of the H21 highway connecting Donetsk to Luhansk and the M04 highway connected Luhansk to the Russian border.
"The control of the M-04 highway near Luhansk by the firepower of the anti-terrorist operation forces will make the delivery of 'humanitarian aid' from Russia to that city impossible if the Russian Federation decides to illegally bring it in through territory controlled by the rebels," Tymchuk said in a statement.
The Russian humanitarian convoy arrived at the border on Friday in an area where most of the Ukrainian side is controlled by rebels.
Ukrainian defence officials said 41 Ukrainian border service representatives and 18 customs officials had begun inspecting the aid on the Russian side, and a Russian journalist traveling with the convoy tweeted a photograph of a car with the International Committee of the Red Cross logo.
Source: The Guardian