Russian troops captured a strategically important former airfield in the south of Ukraine on Saturday, and may continue from there towards Mariupol during the third day of fighting.
Mariupol is close to the eastern Ukrainian separatist areas and is the last major port under government control on the Sea of Azov.
Ukrainians are fighting hard against Russian forces but tens of thousands of Russian troops have now entered Ukraine, according to an estimate by Ukrainian President Volodymyr Zelensky.
Fears in Kiev are growing that Russian troops will target the capital and on Saturday, Ukrainian authorities distributed weapons to the city's residents.
A total of 25,000 automatic weapons, 10 million cartridges and anti-tank weapons have been handed out, Interior Minister Denys Monastyrsky said in a video released on Saturday.
Kiev also extended its night curfew, to apply from 5 pm (1500 GMT) on Saturday to 8 am the next morning, Mayor Vitali Klitschko said. Kiev's metros meanwhile have halted operations as residents use the stations as shelters during air raids.
In a further effort to halt the Russians' advance, the Ukrainian Road Administration called for all road signs to be dismantled, while the Ukrainian army called on the population to stop the Russians in every possible way.
Outside of Kiev, the Ukrainian Defence Ministry said Russian air attacks struck the north-eastern city of Sumy, Mariupol in the south and Poltava in the east.
Russia said it captured the south-eastern Ukrainian town of Melitopol, near the Sea of Azov, and that Moscow-backed separatists had made territorial gains in the Donbass region.
Russian troops also blew up a dam built by Ukraine that had cut off the important North Crimean Canal from the Dnipro river, ending water supplies to Crimea since 2014, army television station Zvezda reported on Saturday.
Earlier, both Russia and Ukraine released figures on the war's toll in terms of lives and infrastructure, although the information could not be independently verified.
Russia has crippled the operations of more than 800 Ukrainian military infrastructure sites, including airfields, command posts, anti-aircraft missile systems and radar stations, the Defence Ministry said.
Moscow insists it is only going after military targets - despite allegations to the contrary from Kiev and witnesses on the ground - and says it is Ukrainian forces that are shelling residential areas in Donbass.
Ukraine's Defence Ministry said some 3,500 Russian soldiers had been killed and 200 others captured.
In addition, it said 14 planes, eight helicopters and 102 tanks as well as more than 530 other military vehicles were destroyed.
According to the Ukrainian government, at least 198 civilians have been killed and 1,115 people injured nationwide, including 33 children, after three days of attacks by Russian ground and air forces. Three children were among the dead, according to Health Minister Viktor Liashko.
At least six ethnic Greeks were killed and six others injured in a Russian airstrike on Sartana in south-eastern Ukraine, the Greek Foreign Ministry said, condemning the act. Athens has summoned the Russian ambassador for Sunday.
US: Russian advance at slow pace
However, Russia's military offensive is making slower progress than Moscow expected, according to a senior US Defence Department official.
"They're meeting more resistance than they expected," the Pentagon representative said in a briefing for journalists. The troops had not advanced "as fast as ... they anticipated they would be able to do." He qualified, however, that Russia was so far still holding back a large proportion of its soldiers stationed near Ukraine.
The US government believes Russia has more than 150,000 troops massed around Ukraine.
Meanwhile, growing numbers of Ukrainians fled the violence. On Saturday, the UN refugee agency put the number of all Ukrainian refugees fleeing to neighbouring countries at 100,000.
Former boxing star Wladimir Klitschko, brother of the mayor of Kiev, made an urgent appeal to the world community for help for Ukraine.
German weapons to Ukraine
Berlin reversed its ban on sending lethal weapons and approved the delivery of 400 German-made anti-tank weapons from the Netherlands to Ukraine. It also authorized Estonia to deliver several artillery pieces from old East German stocks to Ukraine.
Belgium said it would provide weapons and fuel. "Belgium will also deliver 2,000 machine guns to the Ukrainian army," Belgium's Prime Minister Alexander de Croo tweeted. In addition, Belgium will send 300 soldiers to Romania.
Italy will send four more fighter jets to Romania to strengthen NATO's south-eastern flank, Defence Minister Lorenzo Guerini announced in Rome on Saturday.
Baltics close airspace to Russian aircraft
Airlines also cut flights to Russia. Latvian airline Air Baltic will avoid Russian airspace for a month, the state-owned company announced in Riga on Saturday. The Baltic states also want to close their airspace to aircraft from Russia because of its invasion of Ukraine.
Some measures appeared to take effect as French authorities intercepted a Russian freighter ship in the English Channel, after EU sanctions were imposed.
Amid fears that Moscow's aggressions could target further countries in the region, French President Emmanuel Macron reaffirmed his support for the EU's eastern neighbours Moldova and Georgia in the event of a Russian attack.
However, Moscow insisted it would continue its onslaught.
"The military operation to protect the Donbass will be carried out fully and until all results are achieved. No more and no less," according to former president Dmitry Medvedev.