Russian forces have launched a "fierce," large-scale attack on the eastern Ukrainian city of Avdiivka, intensifying the fighting there, but they have so far been unable to make significant progress, according to Ukrainian officials, analysts and geolocated footage shared on social media.

"The fighting has been going on for four days," Vitalii Barabash, the head of the Avdiivka city military administration, told Ukrainian national television on Friday. "Fierce and really non-stop. Both small arms battles and artillery duels."

According to Barabash, Russia has been "firing everything they have available" at the city in a bid to encircle Ukrainian fighters.

"Unfortunately, they are hitting not only the settlements that are, let's say, on the front line, but also further away, at the rear settlements," he said. "They have never gone head-on, but are focused entirely on striking the flanks, from the south and north of the city. They are trying to implement their plan to encircle the city in this way. "

Barabash went on to say that Russia was launching hundreds of continuous attacks on Ukrainian positions in the city in Donetsk oblast, with support from tanks and armored personnel carriers.

"On the first day, 10 (October), when they launched (the offensive), they used a lot of vehicles. On the second day, not so much. And yesterday they used armored vehicles again, they were moving in columns, they have a lot of vehicles and personnel, they bring in fresh people," he said.

Geolocated footage shared on social media by reputable open-source intelligence (OSINT) accounts showed several Russian vehicles under attack by Ukrainian forces, using artillery, US-donated Javelin shoulder-launched missiles and also drones. Some suggested Russia had lost more than a dozen armored vehicles in the attack.

CNN could not independently verify those videos and what they purported to show, but Ukrainian officials have said so far they have been able to hold back the Russian push, destroying a large number of vehicles in the process.

"It's very difficult, very tense, but they (the Ukrainian military) have been standing firmly in their positions for four days," Barabash added. "I am sure they will hold out. They are not human beings, they are titans."

Ukrainian President Voloydymr Zelensky also said his country's troops were keeping Russian forces at bay.

"Avdiivka. We are holding our ground," Zelensky said on Telegram Thursday. "It is Ukrainian courage and unity that will determine how this war will end. We must all remember this."

Later, in his nightly address, Zelensky said units along the eastern front line had "destroyed hundreds of (the) occupier's armored vehicles" in the past few days alone.

"I am grateful to every warrior and every unit for their resilience," he added.

The attack on Avdiivka comes as Ukraine's summer counteroffensive continues to move much more slowly than initially anticipated.

Some analysts had initially suggested the Russian move was designed to force Kyiv to divert some of the forces it had been using for its attacks along the southern and eastern front lines, but Ukrainian officials say the goal is actually to make advances while Kyiv is focused elsewhere.

"The enemy sees Avdiivka as an opportunity to gain a landmark victory and turn the tide of the war," the spokesperson for the southern frontline group of forces, known as "Tavria," Oleksandr Shtupun, told Ukrainian television on Thursday. "While at the time of the full-scale invasion, Avdiivka was seen by the enemy as something insignificant, today the capture or encirclement of Avdiivka is perhaps the most that they can achieve at this stage."

"That is why the enemy is actively using aviation and continuing its offensive," he added.

Imagery geolocated by highly regarded OSINT accounts suggested Russia was able to make some gains along the flanks of the city, but was not able to achieve a major breakthrough.

"Russian forces have not secured any major breakthroughs near Avdiivka as of October 12 and are unlikely to immediately cut off Ukrainian forces in the city," the Institute for the Study of War (ISW) said in its daily bulletin on Friday. "ISW estimates that Russian forces have captured 4.52 square kilometers of territory from different directions around Avdiivka since October 10."

CNN could not independently verify those videos or the analysis of that footage made by the ISW.

Despite the lack of progress, Russian attacks are taking a toll on the roughly 1,600 civilians who still live in the embattled city.

"During the escalation, we stopped supplying humanitarian aid and food to the city. We are only trying to ensure evacuation. In principle, the city has everything, including food, hygiene and medical supplies in sufficient quantities with a reserve for a couple of months, that's for sure," Barabash explained. "Our hospital was heavily shelled with cannon artillery, and two rockets also hit the central building. There is damage, serious damage to the hospital. But everyone is alive."

Over the past four days, at least one person was killed and four were injured. Another two, Barabash said, were still missing, suspected to be stuck underneath the rubble of a collapsed building.

"We can say 100% that people died under the rubble, we just don't see the bodies physically," he added.

Avdiivka, a city very close to the Donetsk city airport, had already been the front line between Ukrainian forces and Russian-backed separatists since 2014. It is seen by Ukrainian and Russian forces as a heavily fortified stronghold, with entrenchments built up over the past eight years.

Some analysts and officials have compared Avdiivka to the city of Mariupol, suggesting that even if encircled, it would be able to hold out against Russian forces for several weeks.