Moscow ordered its troops to advance in Ukraine "from all directions" while the West responded late Saturday with sanctions that sought to cripple Russia's banking sector.
Ukrainian officials said 198 civilians, including three children, had been killed since Russia invaded on Thursday, and warned Russian saboteurs were active in Kyiv where explosions forced residents to flee underground.
Moscow said it fired cruise missiles at military targets, continuing the offensive after accusing Ukraine of having "rejected" talks.
But on day three of Russia's invasion, defiant Ukrainian President Volodymyr Zelensky vowed his country would never give in to the Kremlin as Washington said the invading force had a "lack of momentum."
Ukraine's army said it held back an assault on the capital — but was fighting Russian "sabotage groups" that had infiltrated the city.
"We will fight until we have liberated our country," Zelensky said in a video message.
He earlier said Ukraine had "derailed" Moscow's plan to overthrow him and urged Russians to pressure President Vladimir Putin into stopping the conflict.
In retaliation for the invasion, the West said it would remove some Russian banks from the SWIFT bank messaging system, and froze Central Bank assets — essentially crippling Russia's trade with most of the world.
Meanwhile, the Pentagon estimates that roughly half of the more than 150,000-strong invasion force built up by Moscow on Ukraine's borders in recent months is now inside the country.
But there had been a "lack of momentum over the last 24 hours," and the Russian military had still not gained air superiority over the country, a U.S. official said.
'I was trembling'
Ignoring warnings from the West, Putin on Thursday unleashed a full-scale invasion that the UN refugee agency says has forced almost 150,000 people to flee to neighbouring countries.
Tens of thousands more are estimated to be displaced within Ukraine.
In neighboring Romania, Olga, 36, was among hundreds to have crossed the Danube river with her three young children to safety.
"My husband came with us as far as the border, before returning to Kyiv to fight," she said.
Thousands have made their way to Poland by train.
"Attacks were everywhere," said Diana, 37, who fled the Ukrainian capital.
"My mother is still in Kyiv."
As air raid sirens rang out in the capital, residents sought sanctuary in subway stations and cellars, while Zelensky announced a baby girl had been born on the metro.
The city said anyone outside after 5:00 p.m. (1500 GMT) would be considered "members of the enemy's sabotage and reconnaissance groups."
The curfew will last until 8:00 a.m. Monday.
Yulia Snitko, a pregnant 32-year-old, said she had sheltered in the basement of her Kyiv apartment block on Friday night, fearing premature labour.
"It was more than one hour of huge explosions. I was trembling," she said.
Thousands around the world demonstrated their solidarity with Ukraine on Saturday.
Zelensky said he asked UN Secretary-General Antonio Guterres to strip Russia of its vote at the UN Security Council as punishment for the invasion.
Earlier, he thanked "partners" for sending weapons and equipment, while Washington announced $350 million of new military assistance.
Berlin said it would send Kyiv 1,000 anti-tank weapons and 500 Stinger missiles, in a major U-turn from its longstanding policy of not exporting weapons to war zones.
Paris said it would deliver more arms to Ukraine.
'Paralyze' Russian assets
The European Union said it would "paralyze" Russian central bank assets by banishing "certain" Russian banks from the global SWIFT system.
The move seeks to cripple Russia's trade with most of the world.
Germany had previously resisted the SWIFT removals over concerns Russia could cut off key gas supplies.
The Kremlin has so far brushed off sanctions, including those targeting Putin personally, as a sign of Western impotence.
Speaking in Washington Saturday, a senior U.S. official said the measures would turn Russia into a "pariah," adding that a task force will "hunt down" Russian oligarchs' "yachts, jets, fancy cars and luxury homes."
The UN Security Council will convene Sunday afternoon to vote on a resolution calling for a special session of the General Assembly over the Russian invasion of Ukraine, diplomats have said.
NATO said it will deploy its 40,000-strong rapid response force to Eastern Europe for the first time, but stressed it will not send forces to Ukraine.
On the ground Saturday, AFP reporters in Kyiv heard occasional blasts of what soldiers said were artillery and Grad missiles being fired, with loud explosions reported.
Emergency services said a high-rise apartment block was hit Saturday night, with a hole five floors high blown out of the building.
Kyiv Mayor Vitali Klitschko said the building had been hit by a missile, and that Russian forces were battling to advance from the northwest and west of the city.
"The enemy has not broken into the city, but sabotage groups are operating in Kyiv," he said later.
An oil depot near Vasylkiv town (18 miles southwest of Kyiv) was targeted overnight causing a huge fire, according to the Special Communications Service on Sunday, which added a gas pipeline in eastern Kharkiv had also been hit.
Putin has said Russia is defending Moscow-backed separatists in eastern Ukraine.
The rebels have been fighting Ukrainian government forces for eight years in a conflict that has killed more than 14,000 people.
Putin called the current conflict a "special military operation" and Russia's communications regulator on Saturday told independent media to remove reports describing it as an "assault, invasion, or declaration of war."
Russia also released images of the Chernobyl nuclear plant, site of the 1986 nuclear disaster, with a masked soldier saying radiation was "under control."