With attempts to restart peace talks stalled, pro-Russian rebels have stepped up attacks in the past week and casualties have mounted, including 13 civilians killed in an attack on a passenger bus, which Kiev blamed on the separatists.
Military spokesman Andriy Lysenko said the army's operation had returned battle lines near the airport to the previous status quo and thus not violated the 12-point peace plan agreed with Russia and separatist leaders last September in Minsk.
"We succeeded in almost completely cleansing the territory of the airport, which belongs to the territory of Ukrainian forces as marked by military separation lines," he said.
Kremlin spokesman Dmitry Peskov said Moscow was concerned by what he called an escalation by Ukrainian forces that did not contribute to peace efforts.
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He later said Ukrainian President Petro Poroshenko had rejected a peace plan contained in a letter Russian President Vladimir Putin sent him on Thursday.
"In recent days, Russia has consistently undertaken efforts as an intermediary in regulating the conflict," Peskov said, according to the ITAR TASS news agency.
It said Putin's letter included a concrete plan for both sides to withdraw heavy artillery.
Russian television channel NTV published the letter on Sunday evening. In it, Putin proposed "urgent measures for the cessation of mutual shelling, and also the rapid withdrawal by the sides in the conflict of means of destruction with a calibre higher than 100 mm".
A Poroshenko spokesman said the Ukrainian president would not comment on the letter this evening.