On Sunday, an unexplained explosion destroyed nine parked cars in a district of Kiev.

Russia’s Foreign Ministry accused Ukraine on Monday of making a disingenuous offer to reinstate the cease-fire negotiated on Sept. 5. The ministry said the authorities in Kiev had first ignored peace overtures in a letter from President Vladimir V. Putin that was sent late last week. Ukraine’s president, Petro O. Poroshenko, proposed an immediate recommitment to a cease-fire in the east. “Ukraine is ready to sign a cease-fire agreement if the sides stick to the Minsk accords,” he said, referring to the talks in Belarus that led to the cease-fire. “Ukraine wants peace.”

Both sides in the conflict concede that what they are now fighting over is chiefly a symbol, and a battered, ugly one at that: the ruins of the airport.

For the Ukrainians, the airport forms the army’s toehold in the rebel capital city, Donetsk, illustrating to residents there that a breakaway region will never really be viable or independent.

For Russia, the continual rebel efforts to seize the ruins achieve substantially the same goal: highlighting the perpetual state of insecurity Ukraine will live in, so long as Russia’s interests are not reckoned with. Russia’s Foreign Ministry issued a statement over the weekend saying Ukraine should voluntarily hand over the airport to separatist control.

European foreign ministers meeting Monday opted to keep economic sanctions against Russia in place, despite suggestions in an internal European Union policy document leaked last week that European nations should seek to revive some cooperation with Russia.

Fighters with the Donetsk People’s Republic, one of the separatist forces, seized control of the airport’s runway and taxiways last week, according to Ukrainian accounts, while the terminal buildings were the setting of bitter, close combat. Pro-Russian groups controlled the second floor and above in the main terminal building, while the Ukrainian forces held lower floors and access tunnels. Stairwells and even holes in the floors became front lines.

In the tank assault on Sunday, Ukraine’s army claimed to have expelled the separatists from the runway, allowing the army to move new forces into the terminal and evacuate casualties.