Ukrainian President Volodymyr Zelenskiy urged citizens to help defend Kyiv as Russian troops advanced on the city, forcing people to seek refuge in shelters or flee.
Authorities had already warned people in capital about advancing Russian forces after missiles struck the city.
Zelenskiy said Russian forces were targeting civilian areas as they advanced with troops and tanks from three sides.
The Defense Ministry early on February 25 told residents to make petrol bombs to repel invading Russian forces and by evening witnesses reported hearing artillery rounds and intense gunfire from the western part of the city.
The president called on Ukrainians to "stop the enemy wherever possible." Zelenskiy previously vowed in a video showing him on the streets of Kyiv with government officials that he would remain in the capital and defend Ukraine's independence.
Mayor Vitaly Klitschko said that five explosions had struck near a major power plant on Kyiv's eastern outskirts. There was no information on what caused them.
Zelenskiy also warned in a video message released early on February 26 on his Telegram channel that Russian troops would attempt to seize the Ukrainian capital during the night.
"The enemy will use all its forces to break our resistance. This night they will storm," he said.
Zelenskiy said earlier on Twitter that there had been heavy fighting, with people killed at the entrance to the eastern cities of Chernihiv and Melitopol, as well as at Hostomel.
Explosions also were heard in Kharkiv in the east near Ukraine's border with Russia, and air raid sirens sounded over Lviv in the west, according to witnesses. Authorities reported heavy fighting in the eastern city of Sumy.
An RFE/RL correspondent in Kharkiv said a column of Russian Grads, which are truck-mounted multiple rocket launchers, was destroyed outside the city. The correspondent reported seeing the body of a Russian soldier at the scene. Other casualties were unknown.
Tens of thousands of Ukrainians, meanwhile, fled to neighboring countries in search of safety.
Those arriving were mostly women, children, and elderly after Zelenskiy signed a decree banning men age 18 to 60 from leaving.
At border crossings in Poland, Ukrainians arrived on foot and by car and train and were greeted by Polish authorities and volunteers offering them food and hot drinks.
Traffic was backed up for several kilometers at some border crossings into Poland, Slovakia, Hungary, Romania, and Moldova.
The European Union will take in all people fleeing Ukraine due to the current conflict, German Foreign Minister Annalena Baerbock said.
“We tried everything so this day wouldn’t come,” she said. “And it came because the Russian president chose it, opted for war and against human lives.”
In the midst of the violence and chaos, Russia and Ukraine signaled an openness to negotiations.
The Kremlin accepted Kyiv's offer to hold talks, but it was not clear that it was a gesture toward a diplomatic solution. Zelenskiy’s spokesman, Sergiy Nykyforov said Ukraine remains "ready to talk about a cease-fire and peace."
Kremlin spokesman Dmitry Peskov said Russian President Vladimir Putin was ready to send a delegation to Belarus's capital for talks with Ukraine.
Peskov told reporters that after the parties discussed Minsk as a possible venue, Ukrainian officials changed course and said they were unwilling to travel to Minsk and would prefer to meet in Warsaw. They then halted further communication, Peskov said.
U.S. State Department spokesman Ned Price said Russia's offer of talks was an attempt to conduct diplomacy "at the barrel of a gun" and that Putin's military must stop bombing Ukraine if it was serious about negotiations.
WATCH: A woman in the southern Ukrainian town of Henichesk berates a Russian soldier, asking why he came to her country "with a weapon."
Putin on February 25 called on the Ukrainian Army to overthrow the government, describing its leaders as "terrorists" and "a gang of drug addicts and neo-Nazis."
Putin made the baseless statement in a televised address in which he also accused "Ukrainian nationalists" of deploying heavy weapons in residential areas of major cities to provoke the Russian military.
"They say that civilian objects are not a target for them. But this is another lie of theirs. In reality, they do not distinguish between areas in which they operate," Zelenskiy said in a video address early on February 25.
"Ukrainians are demonstrating heroism," he said, adding that "all our forces are doing everything possible" to protect people.
The Ukrainian leader said earlier that his country was facing Russia's assault "alone."
"This morning, we are defending our state alone. Like yesterday, the world's most powerful forces are watching from afar. Did yesterday's sanctions convince Russia? We hear in our sky and see on our earth that this was not enough," he said.
War Damage In Ukraine, Seen From Above And On The Ground
Zelenskiy said 137 civilians and military personnel had been killed in the Russian attacks on the first day.
He called them "heroes" in a video address released early on February 25 in which he also said more than 300 people were injured in less than 24 hours of fighting.
Ukraine's Defense Ministry later on February 25 said that more than 1,000 Russian servicemen had been killed so far in the conflict. "Russia has not suffered so many casualties during the fighting in any of its armed conflicts since its inception," it said in a statement.
"Russian mothers send their sons to certain death, because the Ukrainian armed forces hold the lines and will defend their country against the occupiers," the statement read.
The Russian Defense Ministry, on the other hand, has said there had been no casualties. Neither claim could be independently verified.
The United Nations said 25 civilians had been killed and 102 wounded, figures that were likely to be a "significant underestimate."
The Ukrainian military reported significant fighting in the area of Ivankiv, about 60 kilometers northwest of Kyiv.
"The hardest day will be today. The enemy's plan is to break through with tank columns from the side of Ivankiv and Chernihiv to Kyiv," Interior Ministry adviser Anton Herashchenko said on Telegram.
Zelenskiy said he understood Russian troops were coming for him but vowed to stay in Kyiv.
"[The] enemy has marked me down as the No. 1 target," Zelenskiy said in a video message. "My family is the No. 2 target. They want to destroy Ukraine politically by destroying the head of state.
"I will stay in the capital. My family is also in Ukraine," he said.
"They're killing people and turning peaceful cities into military targets. It's foul and will never be forgiven," Zelenskiy said.
The president said all border guards on the Ukrainian Black Sea island of Zmiinyi (Snake) in the Odesa region were killed. All of them will be posthumously awarded the title of Hero of Ukraine, he said.
Ukraine's border guard service earlier in the day reported that the island had been taken by Russian forces.
Russia began its invasion before dawn on February 24, unleashing air strikes on cities and military bases and sending in troops and tanks from multiple directions. The deputy defense minister reported heavy Russian shelling in the eastern Donetsk region.
Ukrainian officials said that during the first days of the hostilities they had lost control of the decommissioned Chernobyl nuclear power plant, scene of the world's worst civilian nuclear disaster.
Heavy fighting also took place in the regions of Sumy and Kharkiv in the northeast and Kherson and Odesa, Ukraine's most important seaport, in the south.
Speaking on February 25, British Defense Secretary Ben Wallace said Russia intends to take the whole of Ukraine but that the Russian Army failed to deliver on the first day of its invasion.
For his part, French Foreign Minister Jean-Yves Le Drian accused Putin of trying to destroy Ukraine's statehood, warning that the "security" of its president was at risk.
Meanwhile, Putin told his Chinese counterpart, Xi Jinping, in a call on February 25 that Russia is willing to hold high level talks with Ukraine, China's Foreign Ministry said.
China has refused to call Russia's action in Ukraine an "invasion" or criticize Moscow, despite intensifying assaults from Russia's military.
The EU said on February 25 that Putin was looking to destroy Ukraine and that his actions were comparable to those of the Nazis in World War II.
"He is talking about de-Nazifying Ukraine, but he behaves like Nazis. So this is all in his head," EU spokesman Peter Stano told reporters in Brussels.
