KYIV, Ukraine—Ukrainian forces and thousands of freshly recruited volunteers regained control of Kyiv’s streets after Russian troops and undercover units in civilian clothes tried to enter the city in the early hours of Saturday, while Russian airstrikes, airborne landings and armored advances continued throughout the country.

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KYIV, Ukraine—Ukrainian forces and thousands of freshly recruited volunteers regained control of Kyiv’s streets after Russian troops and undercover units in civilian clothes tried to enter the city in the early hours of Saturday, while Russian airstrikes, airborne landings and armored advances continued throughout the country.

On the third day of the war that Russian President Vladimir Putin unleashed with the aim of overthrowing Ukraine’s elected government and ending its alignment with the West, Ukrainian forces fought fiercely on all fronts, with each side asserting it had inflicted heavy losses on the other.

Read live updates on Russia’s invasion of Ukraine

President Volodymyr Zelensky recorded a video address from the street outside the presidential headquarters in Kyiv, urging Ukrainians to keep fighting and denying Russian reports that he had called on his forces to lay down arms.

“Truth is on our side. This is our land, our country, our children, and we will keep defending them all,” he said. “Glory to Ukraine.”

A rapid Russian victory in the biggest war in Europe for decades would drastically change the geopolitical balance on the continent, giving Mr. Putin control of strategically vital swaths of the former Soviet Union’s territory and placing Russia’s armies on the doorstep of the North Atlantic Treaty Organization.

European and U.S. officials are increasingly concerned that Mr. Putin’s broader goal of revising the ending of the Cold War, restoring Moscow’s former sphere of influence in Europe’s east, won’t stop at Ukraine, a fear that could force a rethink of NATO’s military stance and Europe’s energy supplies, which depend in large part on Russia. Mr. Zelensky has constantly reinforced that message, saying that Ukrainians are fighting and dying not just for their own country but for all of Europe.

Traffic jams have choked roads in Kyiv as people try to flee Russia's pressing assault. WSJ's Brett Forrest documented his long car journey out of the Ukrainian capital while traveling to cover the war. Photo: Ethan Swope/Bloomberg News The Wall Street Journal Interactive Edition

If fierce Ukrainian resistance leads to a long and bloody war—or forces Mr. Putin to seek to end the fighting without achieving his goals—the setback could threaten both his hold on power in Moscow and his drive to restore Russia as a global power.

Mr. Zelensky, in an address on Saturday, said that Russia has failed in its quest to quickly replace him with a puppet regime and that Ukrainian soldiers were holding the line throughout the country. He called on Ukrainians abroad and foreign volunteers to join the fight. “Everyone who can, come back to defend Ukraine,” Mr. Zelensky said. “All the friends of Ukraine who want to come join us, come here too—we will give you weapons.”

On Friday, the biggest thrust of Russian forces, pouring in from the north, targeted Kyiv, an ancient city that was home to around three million people before Russian bombardments triggered a mass exodus of people toward western Ukraine, which is safer. Many who remained in the city spent the night in bomb shelters and underground subway stations.

President Volodymyr Zelensky recorded a video address in Kyiv urging Ukrainians to keep fighting.

Photo: /Associated Press

Ukrainian civilians fleeing westward have been stuck in long lines of cars near the border with Poland. Many people have abandoned their cars and walked to the border for many hours in chilly weather, carrying children and a few belongings.

Ukraine’s Health Ministry said Saturday that 198 Ukrainian civilians, including three children, had been killed since the Russian invasion began, and 1,115 injured.

“We knew that the night would be difficult because the Russian Federation would use all its resources and reserves to inflict on us maximum damage in the maximum number of locations,” Mr. Zelensky’s adviser, Mykhailo Podolyak, said early Saturday. “Kyiv is their priority number one because the main declared goal of the Russian operation is the annihilation of Ukraine’s political and military leadership. That is why they are pouring the maximum number of Russian troops toward Kyiv.”

Explosions and gunfire rocked Kyiv as Russian troops intensified attacks on Ukraine’s capital. Residential areas were hit and people sought refuge, while Ukrainian President Volodymyr Zelensky called for help from Western leaders. Photo: Oleksandr Ratushniak/AP The Wall Street Journal Interactive Edition

A Russian column that attempted to advance from the West, on the highway linking Kyiv to Lviv, was destroyed in nighttime fighting inside Kyiv, witnesses said. Bodies lay on the ground, amid the smoldering remains of armored vehicles and trucks. Presumed Russian infiltrators, traveling in civilian vehicles, were also gunned down by Ukrainian troops as they tried to approach the Ukrainian Parliament building, the witnesses said. Intense firefights were reported in other locations throughout the capital.

After daybreak on Saturday, Ukrainian regular troops and volunteers of the newly formed Territorial Defense force regained the upper hand, erecting roadblocks, firing positions and other fortifications around the city, particularly in the government district and near bridges spanning the Dnipro river. Trucks accompanied by police ferried ammunition as civilians lined up patiently in grocery stores, at pharmacies and teller machines.

A large supermarket on Kyiv’s Antonovycha street was well stocked, with fresh bread, pineapples and Italian cheese, and some of the checkout lanes still accepted Apple Pay. A handful of basement bars reopened as makeshift shelters, serving espressos before the 5 p.m. curfew kicked in. At one bar, customers were asked to show their passports to prove that they weren’t Russian citizens.

The biggest lines in the Ukrainian capital were at the recruitment centers for the Territorial Defense. At one sports facility converted for this purpose, several hundred volunteers, commanded by career military officers, loaded crates of ammunition into civilian vehicles and sped off to their positions.

Volunteer fighters lined up Saturday at a Territorial Defense mobilization point in Dnipro, eastern-central Ukraine.

Photo: Mykola Miakshykov Ukrinform/dpa/Zuma Press

Outside, hundreds more aspiring recruits, including women, patiently waited their turn in a line that snaked around the building. “I never expected so many would turn up. The whole city has risen up now,” one of the officers at the site said. “A bit too late, but better late than never.”

Concerned about Russian infiltrators and spies, members of the Territorial Defense didn’t allow photography and didn’t provide their names. The volunteers said they had no choice but to fight now that Russian forces were on Kyiv’s doorstep.

“A Russian rocket hit a building near my home this morning. This was the last straw for me, and now it’s time to take up arms. Everyone in this city who wanted to escape has already fled,” said one of the new recruits, a 35-year-old IT specialist.

“There is nowhere to run and no point in hiding. We just have to repel the invaders and send them back where they came from,” said another, a human-resources specialist.

South of Kyiv, Russian airborne troops attempted a landing in the strategic town of Vasylkiv, the location of a Ukrainian military airfield. Firefights broke out during the night but by morning hundreds of Ukrainian troops and irregular volunteers armed with assault rifles patrolled Vasylkiv’s main road. Along the highway running between Kyiv and Odessa near Vasylkiv, security forces and local volunteers wearing armbands were looking for stray Russian troops who might be hiding in the woods.

Ukrainian soldiers said they had driven off most of the Russian landing force in Vasylkiv. Kyiv also said Ukrainian forces had downed a Russian Il-76 transport plane full of airborne troops near Vasylkiv. That claim couldn’t be independently confirmed. In the late morning, contrails of two jet fighters engaging in a dogfight could be seen in the blue skies above the town.

Intense fighting also went on through the night near the southern cities of Odessa, Kherson, Mykolaiv and Mariupol, Mr. Podolyak said.

On Friday, Moscow signaled an openness to talks with Kyiv. But shortly after, Mr. Putin excoriated Mr. Zelensky, calling him a terrorist and urging Ukraine’s military to oust him, dimming prospects for diplomacy.

Russia’s continued bombardment of Ukraine has forced many to make the difficult choice between fleeing the country or staying put. WSJ’s Brett Forrest in Kyiv, which was increasingly targeted, explains how people are weighing their options. Photo: Vadim Ghirda/AP The Wall Street Journal Interactive Edition

Mr. Zelensky is expected to speak to several world leaders later on Saturday, Mr. Podolyak said. On Friday, Mr. Zelensky spoke by phone with President Biden. A White House official said the call lasted about 40 minutes.

Mr. Zelensky wrote on Twitter, “Strengthening sanctions, concrete defense assistance and an antiwar coalition have just been discussed with @POTUS.”

U.S. Secretary of State Antony Blinken said in a statement Saturday that Washington would provide up to $350 million in additional military aid to Ukraine, including “lethal defensive assistance” to help Kyiv resist Russian armored and airborne forces.

Surveillance footage showed a missile hitting a residential building in Kyiv on Saturday.

Photo: REUTERS

Firefighters extinguished a blaze on Saturday in an apartment building damaged by shelling in Kyiv.

Photo: GLEB GARANICH/REUTERS

Mr. Blinken didn’t say which weapons Washington intended to provide. The U.S. has previously sent Javelin antitank weapons and ammunition, among other battlefield systems. In January, the U.S. also gave approval for Latvia and Lithuania to deliver American-made Stinger antiaircraft missiles to Kyiv.

Mr. Biden authorized the fresh delivery of military aid Friday night and approved up to $250 million for overall assistance to Ukraine. A person familiar with the matter said the administration has asked Congress for $6.4 billion in additional funding for Ukraine aid and defense needs.

Ukrainian volunteer fighters received weapons and training in Kyiv on Saturday.

Photo: Erin Trieb/Bloomberg News

A couple embraced on Saturday at a Ukrainian border crossing to Slovakia, as many Ukrainians fled the war in their country.

Photo: martin divisek/Shutterstock/epa

—Michael R. Gordon contributed to this article.

Write to Yaroslav Trofimov at yaroslav.trofimov@wsj.com