Russia's invasion of Ukraine entered its third day on Saturday, with several major Ukrainian cities being hit by Russian missiles and shells as civilians took to underground shelter or fled their homes.

The Ukrainian military said on Saturday morning that its soldiers had repelled an attack on the capital, Kyiv, following reports of heavy fighting and bombing overnight.

"Last night was difficult, but there are no Russian troops in the city," Kyiv Mayor Vitaly Klitschko said on Saturday morning.

Ukrainian President Volodymyr Zelenskyy posted a video from the center of Kyiv in the early hours of the morning to disprove rumors that the government had already surrendered.

In a later video on Saturday, the president said Ukrainian forces had stopped the Russian advance on the capital.

"We've derailed their plan," he said, adding that the Ukrainian army retains control of Kyiv and the surrounding major cities.

The Ukrainian Defense Ministry said Russian cruise missiles fired from warships in the Black Sea hit the northeastern cities of Sumy and Poltava, as well as the southern port city of Mariupol, where officials also reported heavy fighting on the city's outskirts.

Further fighting was also witnessed in or around the cities of Kherson, Mykolaiv and Odesa, all to the west of Crimea, the Russia-annexed Ukrainian peninsula from which one arm of the Russian invasion was launched.

UN High Commissioner for Refugees Filippo Grandi said on Friday that more than 50,000 people had fled the country already. And reports on Saturday from Polish officials indicate that number has more than doubled. 

Read DW's latest updates from the ongoing conflict.

How has the West responded?

The EU imposed further sanctions on Thursday, including freezing the European assets of Russian President Vladimir Putin and Foreign Minister Sergey Lavrov.

Discussions among EU leaders over the option of kicking Russia out of the international banking transfer system SWIFT are still ongoing, with Germany and Italy both notably blocking such a move.

NATO also activated its Response Force as a defensive measure for the first time in its history amid fears that Moscow that the conflict could spread to neighboring NATO member states.

UN Secretary-General Antonio Guterres called on Russia to return its soldiers "to their barracks." His comments came after Moscow blocked a UN Security Council resolution demanding an end to the invasion.

French President Emmanuel Macron warned on Saturday that Europe needs to be prepared because the war "will last, and all the crises that come with it will have lasting consequences."

What has Putin said about the invasion?

Putin expressed a willingness to hold "high-level" peace talks with Ukrainian officials, going so far as proposing peace talks in Minsk.

His comments came after a phone call with his Chinese counterpart Xi Jinping who expressed support for a negotiated solution to the conflict.

However, shortly afterward the Russian president called on the Ukrainian military to overthrow the democratically-elected Ukrainian government as a condition for peace talks.

Moscow has also vowed to retaliate against Western sanctions.

ab/wmr (dpa, AFP, AP, Reuters)