Ukrainian and Russian troops fight on streets of capital Kyiv
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"I am here. We will not lay down any weapons. We will defend our state, because our weapons are our truth," Zelensky said, as Russia said it had fired cruise missiles at Ukraine's military infrastructure.
Wearing olive green military-style clothing and looking tired but determined, Zelensky said: "Our truth is that this is our land, our country, our children and we will protect all of this.
"This is what I wanted to tell you. Glory to Ukraine!"
It was the third day since Russian leader Vladimir Putin unleashed a full-scale invasion that has killed dozens of people, forced more than 50,000 to flee Ukraine in just 48 hours and sparked fears of a wider conflict in Europe.
French President Emmanuel Macron warned that the world must brace for a long war.
"This crisis will last, this war will last and all the crises that come with it will have lasting consequences," Macron said at an agriculture fair in France. "We must be prepared".
Body on the pavement
A high-rise apartment block was hit by shelling overnight in Kyiv as the fighting raged, emergency services said.
The authorities said the number of victims was "being specified" and that an evacuation was underway.
They posted a picture online of the tower block with a hole covering at least five floors blasted into the side and rubble strewn across the street below.
Kyiv Mayor Vitaly Klitschko said online that the building had been hit by a "projectile".
In Kyiv's city center, AFP journalists heard loud explosions early Saturday.
"Heavy fighting continues," the State Special Communications Service of Ukraine posted on its telegram account around 0330 GMT.
Earlier Saturday, Ukraine's military said Russia had "attacked one of the military units on Victory Avenue in Kyiv" but that the assault had been "repulsed".
It also reported another incident northwest of the capital.
AFP saw a dead man in civilian clothes lying sprawled on the pavement as nearby medics rushed to help another man whose car was crushed by an armoured vehicle.
Kyiv said 137 people, including soldiers and civilians, have been killed.
Meanwhile, the Defence Ministry said "two enemy targets were shot down" -- identifying them as a Russian SU-25 helicopter and a military bomber -- near the separatist zone in the east.
Earlier, small arms fire and explosions were heard in the capital's northern district Obolonsky as what appeared to be an advance party of Russia's invasion force left a trail of destruction.
Moscow has yet to report on casualties.
Point of no return
The United States, Canada, Britain and the European Union doled out further sanctions on Russia on Friday, including against Putin and Foreign Minister Sergei Lavrov.
The EU foreign policy chief Josep Borrell called it the "harshest" package ever drawn up by the bloc.
The UK government ordered all assets of both men frozen while the United States and Canada will also impose sanctions on the pair, with Washington including a travel ban.
Russia said the sanctions against the pair were "a demonstration of the complete impotence of the foreign policy" of the West.
"We have reached the line after which the point of no return begins," Russian foreign ministry spokeswoman Maria Zakharova said.
Moscow also vetoed a UN Security Council resolution that deplored "in the strongest terms" Russia's invasion, while China, India and the United Arab Emirates abstained.
Putin had earlier described the Ukrainian government as "terrorists" and "a gang of drug addicts and neo-Nazis", urging the country's military to topple Zelensky.
Not real diplomacy
A Kremlin spokesman said Putin was ready to send a delegation to Belarusian capital Minsk "for talks with a Ukrainian delegation".
But the US swiftly dismissed the offer.
After invading Ukraine, "now we see Moscow suggesting diplomacy take place at the barrel of a gun. This is not real diplomacy," State Department spokesman Ned Price said.
The UN said more than 50,000 Ukrainians had fled the country in the past two days, calling for "safe unimpeded access" for aid operations.
Streams of people in cars and on foot were seen crossing into Hungary, Poland and Romania while hundreds camped out in a train station in the Polish border city of Przemysl.
About 100,000 people are believed to be internally displaced.
The US-led military alliance NATO said it was deploying its rapid response forces for the first time to bolster defences on the alliance's eastern flank.
Despite Zelensky calling on Western allies to expel Moscow from the SWIFT banking transfer system, numerous EU countries, including Germany, Hungary and Italy, have been reluctant over fears Russia could cut off gas supplies.
Facebook also unveiled new restrictions, demonetising Russian state media across its platform.