Russian troops launched multiple attacks to the west of recently captured Avdiivka in a bid to force more gains on the battlefield, a Ukrainian army spokesperson said Sunday.
Kyiv also announced it had opened a war crimes investigation after two separate reports of Russian troops shooting captured Ukrainian soldiers emerged.
Facing manpower and ammunition shortages, Ukraine was forced to withdraw from the industrial hub in the eastern Donetsk region, handing Moscow its first major territorial gain since May 2023.
"The enemy is trying to actively develop its offensive," Dmytro Lykhoviy, a spokesperson for the Ukrainian army commander leading Kyiv's troops in the area, said on state TV on Sunday.
Ukraine's general staff reported 14 failed Russian attacks on the village of Lastochkyne, around two kilometres (one mile) to the west of Avdiivka's northern edge.
"But our considerable forces are entrenched there," Lykhoviy said.
He also reported failed Russian attacks near the villages of Robotyne and Verbove in the southern Zaporizhzhia region -- one of the few places where Ukraine managed to regain ground during last year's counter-offensive.
He said it would be "very difficult" for Russia to break through there, given heavy Ukrainian defensive lines and natural conditions of the terrain.
"The situation in the Zaporizhzhia sector is stable... No positions have been lost," he said Sunday on state TV.
"The enemy was kicked in the teeth and retreated," he added.
Russian President Vladimir Putin on Saturday hailed the capture of Avdiivka as an "important victory" for his troops, just days ahead of the second anniversary of the invasion.
The battle for Avdiivka was one of the bloodiest of the two-year war, drawing comparisons with Russia's assault on Bakhmut, which it captured last May at the cost of tens of thousands of soldiers.
Avdiivka had symbolic importance to both Kyiv and Moscow -- seen as a marker of Ukrainian resistance after it briefly fell to Russian-backed separatists in 2014.
Ukrainian President Volodymyr Zelensky said the decision to withdraw was taken to save as many lives as possible among his troops.
Russia's capture of the town has raised fears its forces could now try to advance further into the Donetsk region, which it claims to have annexed.
In the village of Novooleksandrivka some 30 kilometres west, local Vadym told AFP that, for now, he was staying put with his wife and child, born one week ago.
The 22-year-old said shelling by the advancing Russian forces was "constant".
Around 200 people remain, but the attacks had not yet pushed him to leave with his family.
"I hope it will stop. And if it doesn't stop, we will try to leave."
Kyiv's newly installed commander-in-chief Oleksandr Syrsky vowed Sunday his forces would "eventually return to our Ukrainian Avdiivka".
Concerns are growing in Kyiv and the West over Ukraine's ability to thwart a renewed Russian offensive without unlocking a stalled $60-billion US aid package.
Ukraine's Prosecutor General said Sunday it had opened an investigation after the army posted footage of what it said was a Russian soldier shooting two Ukrainian soldiers at point-blank range.
The prosecutor's office said it was investigating possible war crimes based on the footage and said the incident happened near the village of Vesele in Ukraine's Donetsk region.
AFP could not verify the authenticity of the video, its location or when it was shot.
Prosecutors also announced a separate investigation into reports of the alleged execution of six wounded Ukrainian soldiers left behind during Kyiv's withdrawal from Avdiivka.
There was no response from Russia to the allegations.
The army has already said some Ukrainian soldiers were captured during the hasty retreat.
Moscow and Kyiv have several times accused each other of violating international humanitarian law by killing prisoners of war since Russia invaded.
The United Nations has documented cases of summary executions of captured Ukrainian soldiers as well as torture during the two-year war.
