Ukrainian troops are recapturing towns east of the capital Kyiv and Russian forces who had been trying to seize the city are falling back on their overextended supply lines, Britain's Defense Ministry said Friday.

A month into their assault, Russian troops have failed to capture a major Ukrainian city. An offensive that Western countries believe was aimed at swiftly toppling Ukrainian President Volodymyr Zelenskyy's government has been halted at the gates of Kyiv. Battlelines there have been frozen for weeks with Russian columns threatening Kyiv from the northwest and the east. But in an intelligence update on Friday, Britain described a Ukrainian counteroffensive that had pushed the Russians far back.

Ukrainian counterattacks and Russian forces falling back on overextended supply lines have allowed Ukraine to reoccupy towns and defensive positions up to 35 kilometers (21 miles) east of Kyiv, the update said. It noted that Ukrainian forces were also likely to try to push the Russians back on the other main axis threatening Kyiv from the northwest, while in the south, Russia could still be planning to attack the port of Odessa after abandoning efforts to take Mykolaiv.

The Ukrainian military said its troops were repelling Russian forces trying to fight their way into Kyiv. Troops were also still holding on to the city of Chernihiv, northeast of Kyiv, hindering a Russian advance in the direction of the capital.

Russia said Friday it had destroyed the largest remaining military fuel storage site in Ukraine, attacking it with Kalibr cruise missiles.

"On the evening of March 24, Kalibr high-precision sea-based cruise missiles attacked a fuel base in the village of Kalynivka near Kyiv," the Russian Defense Ministry said in a statement, adding that it was Ukraine's largest remaining military fuel storage facility, supplying troops in the central part of the pro-Western country.

Since the start of Moscow's military action in Ukraine, Russian troops have destroyed more than 260 drones, over 1,580 tanks and other armored vehicles, and 204 anti-aircraft weapons systems, the ministry said. While Ukrainian forces have stalled the initial Russian invasion and even launched some successful counterattacks, there are early signs that both sides are digging in for a long and bloody war that neither can easily win.

Moscow calls its actions in Ukraine a "special military operation" to disarm its neighbor. Kyiv and its Western allies call it an unprovoked war of aggression and say Russia's true aim was to overthrow the government of what President Vladimir Putin regards as an illegitimate state.

Russians have begun to flee from Hostomel, a Ukrainian presidential adviser Oleksiy Arestovich said.

"They have already begun to depart from Hostomel. We saw the first ones today. They throw equipment, some of them change into civilian clothes, some just leave," he said.

Unable to capture Ukrainian cities, Russia has resorted to pounding them with artillery and airstrikes. The eastern port of Mariupol has been under siege since the war's early days. Tens of thousands of people are still believed to be trapped inside with no access to food, medicine, power or heat. In a part of the city now captured by the Russians, one woman waiting in line to receive food supplies told Reuters her diabetic husband had slipped into a coma and died. He was buried in a flowerbed.

"We are planning on leaving but it's very difficult at the moment," the woman, who gave her name as Alexandra, said. "I can't leave my husband in a flowerbed ... And then we have nowhere to go."

About 20,000 people have answered appeals to flee the Ukrainian city of Boryspil, which is near an international airport, Boryspil Mayor Volodymyr Borysenko said on national television on Friday. He urged others to evacuate, saying the large number of civilians in villages nearby made it difficult for Ukrainian troops to clear Russian forces from the area. Boryspil International Airport is about 30 kilometers east of the Ukrainian capital Kyiv.

Ukraine hoped Friday to make it possible for some civilians who have been trapped in the besieged city of Mariupol to leave in private cars, Deputy Prime Minister Iryna Vereshchuk said. Repeated attempts to arrange safe passage out of the southern port city, which is surrounded by Russian forces, have failed.

Mariupol, which is normally home to about 400,000 people, has been under heavy bombardment for weeks. Civilians trapped there have been sheltering in basements with little food, power or running water.

Those who manage to leave Mariupol will find buses awaiting in the nearby city of Berdyansk which will take them to the city of Zaporizhzhia, Vereshchuk said.

"We will do everything in our power so that buses filled with Mariupol residents reach Zaporizhzhia today," she said.

Ukrainian officials in Mariupol said Friday they feared 300 people could have died in last week's Russian strike on a theater where hundreds were sheltering.

"From eyewitnesses, information is emerging that about 300 people died in the Drama Theatre of Mariupol following strikes by a Russian aircraft," Mariupol city hall wrote on Telegram.

Mariupol city hall said Friday the theater was destroyed in a "cynical" attack and claimed that Russia knew civilians were taking refuge in the building.

In Chernihiv, where an airstrike this week destroyed a crucial bridge, a city official, Olexander Lomako, said a "humanitarian catastrophe" is unfolding as Russian forces target food storage places. He said about 130,000 people are left in the besieged city, about half its prewar population.

While a number of refugees from various parts of the country continued to flock to the train station in Lviv with an aim to leave the state, a group of Ukrainian women was seen carrying arms, readying to go to the front.

Ukraine and Russia exchanged a total of 50 military and civilian prisoners, the largest swap reported yet, Vereshchuk said.

Russian forces fired two missiles late Thursday at a Ukrainian military unit on the outskirts of Dnipro, the fourth-largest city in the country, the regional emergency services said. The strikes destroyed buildings and set off two fires, it said. The number of dead and wounded was unclear.

On the same day, Ukraine accused Moscow of forcibly removing hundreds of thousands of civilians from shattered Ukrainian cities to Russia to pressure Kyiv to give up, while Zelenskyy urged his country to keep up its military defense and not stop "even for a minute."

Lyudmyla Denisova, Ukraine’s ombudsperson, said 402,000 people, including 84,000 children, had been taken against their will into Russia, where some may be used as "hostages" to pressure Kyiv to surrender.

The Kremlin gave nearly identical numbers for those who have been relocated but said they were from the predominantly Russian-speaking regions of Donetsk and Luhansk in eastern Ukraine and wanted to go to Russia. Pro-Moscow separatists have been fighting for control for nearly eight years in those regions, where many people have supported close ties to Russia.

The Ukrainian Navy said it sank a large Russian landing ship near the port city of Berdyansk that had been used to bring in armored vehicles. Russia claimed to have taken the eastern town of Izyum after fierce fighting.

Zelenskyy used his nightly video address to rally Ukrainians to "move toward peace, move forward."

"With every day of our defense, we are getting closer to the peace that we need so much ... We can’t stop even for a minute, for every minute determines our fate, our future, whether we will live."

He said thousands of people, including 128 children, have died in the first month of the war. Across the country, 230 schools and 155 kindergartens have been destroyed. Cities and villages "lie in ashes," he said.

U.S. President Joe Biden meanwhile was due to visit Poland for a firsthand look at the refugee crisis in which nearly a quarter of Ukraine's 44 million people have been uprooted and more than 3.6 million have fled to neighboring states since the Russian invasion on Feb. 24. The West has ruled out intervening on the ground or answering Ukraine's plea for a no-fly zone but has supported Kyiv with hundreds of anti-tank and anti-aircraft weapons that have blasted Russian armored columns and prevented Moscow from taking control of the air.

Biden, in Europe for the series of high-level meetings, gave assurances that more aid was on the way, though it appeared unlikely the West would give Zelenskyy everything he wanted, for fear of triggering a much wider war.