Russia’s renewed ground offensive in Ukraine’s northeast targeted towns and villages with a barrage of artillery and mortar fire, officials said Sunday. Thousands of civilians fled the Kharkiv region as the intense battle capitulated more land to Russian forces across less defended settlements in the so-called contested “gray zone” along the Russian border.

The town of Vovchansk, with a prewar population of 17,000, emerged as a focal point in the battle.

Volodymyr Tymoshko, the head of the Kharkiv regional police, said Russian forces were in the outskirts of the town and approaching from three directions. A Russian tank was spotted along a major road leading to the town, Tymoshko said, illustrating Moscow’s confidence to deploy heavy weaponry.

Evacuation teams worked non-stop throughout the day to take residents, most of whom were elderly, out of harm’s way.

At least 4,000 civilians have fled the Kharkiv region since Friday, when Moscow’s forces launched the operation, Gov. Oleh Syniehubov said in a social media statement. Heavy fighting raged Sunday along the northeast front line, where Russian forces attacked 27 settlements in the past 24 hours, he said.

The Russian Defense Ministry said on Sunday that its forces had captured four villages, in addition to five villages reported to have been seized the day before.

These areas were likely poorly fortified due to the dynamic fighting and constant heavy shelling, easing a Russian advance.

Ukraine’s leadership has not confirmed Moscow’s gains. Instead, they said it was repulsing the attacks and battling for control of the settlements.

Ukrainian President Volodymyr Zelenskyy said halting Russia’s offensive in the northeast was a priority, and that Kyiv’s troops were continuing counteroffensive operations in seven villages around the Kharkiv region.

“Disrupting the Russian offensive intentions is our number one task now. Whether we succeed in that task depends on every soldier, every sergeant, every officer,” Zelenskyy said.

A Ukrainian unit said that they had been forced to retreat in some areas.

Tymoshko said Russian tactics in Vovchansk mirrored those used in the battles for Bakhmut and Avdiivka in the Donetsk region in which heavy aerial attacks were accompanied by droves of infantry assaults.

In a video Saturday evening, the Hostri Kartuzy unit, part of the special forces’ detachment of Ukraine’s national guard, said that they were fighting for control of the village of Hlyboke.

“Today, during heavy fighting, our defenders were forced to withdraw from a few more of their positions, and today, another settlement has come completely under Russian control. As of 20:00, fighting for the village of Hlyboke is ongoing,” the fighters said in the clip.

Analysts say the Russian push is designed to exploit ammunition shortages before promised Western supplies can reach the front line.

On Sunday, U.S. Secretary of State Antony Blinken denounced Russia’s rush into Kharkiv, saying the United States is doing “everything we can to rush this assistance out there.”

“I’m convinced that Ukraine can effectively hold the line in the east, it can continue to press the advantages achieved for itself in the Black Sea, where it’s getting as much out through the Black Sea, feeding the world as it did before the Russian re-invasion of Ukraine, as well as to hold Russian forces at risk, including in Crimea to make it more difficult for them to continue this aggression,” Blinken told “Face the Nation” host Margaret Brennan on Sunday. “We’ve been providing the systems to do that, but it’s a challenging moment. We are not going anywhere, and neither are more than some 50 countries that are supporting Ukraine. That will continue and if [Russian President Vladimir] Putin thinks he can outlast Ukraine, outlast its supporters. He’s wrong.”

Meanwhile, a 10-story apartment block collapsed in the Russian city of Belgorod, near the border, killing at least two people and injuring 20 others. Russian authorities said the building collapsed following Ukrainian shelling. Ukraine has not commented on the incident.