Andriy Lysenko, a spokesman for Ukraine's National Security Council, told reporters today in Kiev that government forces were now in control of "significant parts" of Luhansk, an eastern city just 20 kilometers (12 miles) from the Russian border.
The regional administration said 34 local residents were killed and 29 wounded in the last 24 hours as of noon. Another 9 people were killed and 13 wounded in afternoon shelling, the Donetsk mayor's office said.
He said fighting continued today in Ilovaysk even though government forces had gained control of the town.
Hard-hit Luhansk has been without electricity, running water or phone connections for 18 days due to the fighting between government forces and pro-Russia separatists.
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"I was with my grandmother in the bathroom, because there is a bearing wall in there," said Anna Zyukova, 22. "And then all of sudden, bam-bam."
"We purposely don't take up positions where people live," a rebel commander who identified himself only as 'Chaika' said, a claim that Ukrainian officials have repeatedly dismissed.
The fighting began a month after Russia annexed Ukraine's Black Sea peninsula of Crimea.
The Kiev government also is pursuing diplomatic efforts to resolve the conflict, which the United Nations says has killed more than 2,000 people.
Ukrainian President Petro Poroshenko will host German Chancellor Angela Merkel this weekend in Kiev before meeting next week with Russian President Vladimir Putin in Minsk, the capital of Belarus.
They also attached a yellow-and-blue Ukrainian flag to the top of the 176-meter (580-foot) building.
While Moscow police detained four suspects and charged them with vandalism, the Ukrainian president, welcomed the flag-hoisting over the skyscraper in a video message, calling it a "symbolic" gesture.
He urged Ukrainians all over the world to fly Ukrainian flags at their homes in celebration of the country's Independence Day holiday on Sunday.