A mass operation by Ukrainian troops has retaken most of the strategic Donetsk airport in eastern Ukraine after it nearly fell to Russia-backed rebels, the country’s military leadership said on Sunday.

The early morning assault marked a further intensification of the fighting that has flared up over the past week, with shelling reported near central Donetsk, which has remained mostly unscathed. Both sides have denied their advances around the airport are in violation of the terms of a September ceasefire.

“The decision was taken for a mass operation … We succeeded in almost completely cleaning the territory of the airport, which belongs to the territory of Ukrainian forces as marked by military separation lines,” Ukraine’s national defence council speaker Andriy Lysenko told journalists on Sunday, adding that Ukrainian forces were only firing at rebel positions that had attacked them. Three soldiers were killed and 31 wounded near the Donetsk airport in the past 24 hours, Lysenko said.

Presidential advisor Yury Biryukov wrote on his Facebook page that Kiev’s troops near Donetsk had received an order at 6am to “open concentrated fire on known separatist positions.” The operation came as thousands rallied around Ukraine to mourn the civilian casualties of an attack last week that Kiev has blamed on the separatists. “Haven’t we observed the ceasefire? Haven’t we shown that we support the peace process? Well okay, today we’ll show that we really know how to hit them in the teeth,” Biryukov said.

But LifeNews, a Russian website known for its access to the Kremlin’s security services, reported on Sunday that Kiev’s forces were shelling airport building and said rebels had repulsed four “mass attacks” by Ukrainian foot soldiers and 15 tanks in the morning. The separatist leaders had claimed in recent days that their forces had taken the airport.

Alexander Zakharchenko, head of the separatist Donetsk People’s Republic, told Russian news agencies on Sunday that rebel-held Donetsk and Luhansk were being shelled by Ukrainian forces and accused Kiev of trying to restart the war. The republic’s defence ministry told Interfax that “almost all districts of Donetsk” were under fire and said shells had fallen near residential buildings in the city centre. Journalists in Donetsk reported incoming and outgoing fire and tweeted photographs of rebel armour on the move and damage from shelling.

The Donetsk airport has remained a main area of contention despite the ceasefire that has been violated by both sides. Fighting resumed near Donetsk and Luhansk following a brief lull before New Year’s and has intensified over the past week. Although the control tower collapsed last week and the terminals and runways have been severely damaged by shelling, the airport holds great symbolic and strategic importance for both sides.

The Russia-backed Donetsk People’s Republic said in a statement on Friday its forces had taken “control over the territory of Donetsk airport and its surroundings” but admitted that “about 10 Ukrainian soldiers” remained in the terminal. Connected to farther back positions by underground utility tunnels, the Ukrainian troops in the airport – popularly known as “cyborgs” for their resilience – have held the bottom floors of the main terminal even as rebel fighters have taken over the top floor and surrounding areas.

Thousands in Kiev and other cities on Sunday afternoon attended a “requiem” march for the 12 bus passengers killed in an apparent separatist attack on a Ukrainian military checkpoint near Volnovakha in eastern Ukraine on Tuesday. President Petro Poroshenko and prime minister Arseny Yatseniuk joined the rally-goers in holding candles, flowers and signs reading “Je suis Volnovakha,” a reference to the “Je suis Charlie Hebdo” signs popular after the recent attack on the Paris newspaper.

“We won’t give up a single shred of Ukrainian land! We will take back Donbass,” Poroshenko, referring to eastern Ukraine, told the marchers on Maidan Square, where protests and clashes with police led to the fall of president Viktor Yanukovich last winter.A small group rallied at the Ukrainian embassy in Moscow in solidarity with the Kiev march, while the “anti-Maidan” protestors who have increasingly come out oppose similar events in recent months gathered nearby.

The Donetsk People’s Republic leadership has denied any role in the Volnovakha attack and argued the casualties were caused by a mine.

But a video shot at the checkpoint shows what are likely Grad rockets striking near the road more than a dozen times, then pans to the damaged bus stopped next to a black crater in the snow, suggesting a separatist rocket attack was responsible for the carnage.

A preliminary report from the scene by Organisation for Security and Co-operation in Europe found that the 12 dead and 17 wounded passengers had been hit by shrapnel from a nearby rocket impact.