Ukraine agreed to have talks with Russia on the Belarusian-Ukrainian border, the office of Ukrainian President Volodymyr Zelensky said on Sunday via social media, Xinhua News Agency reported.
The office said that the talks would be held without preconditions and are the result of a phone call between Zelensky and Belarusian President Alexander Lukashenko earlier on Sunday.
The announcement came shortly after Russian President Vladimir Putin ordered Russian nuclear forces put on high alert in response to what he called "aggressive statements" by leading NATO powers.
Russian Defense Ministry spokesman Igor Konashenkov said on Sunday that Russian troops fired cruise missiles at Ukrainian military targets.
There are reports of fighting in the streets of Kharkiv, as Russian troops moved into the city in the morning, local officials said.
Social media footage appears to show some Russian units in Kharkiv. There are photos appearing to show at least two Russian "Tiger"-small, all-terrain, infantry-mobility-vehicles on fire.
On Sunday morning, Kharkiv officials warned locals to stay in shelters and off the streets.
In the west of the center of Kyiv, the capital, a blast was heard in the morning after an air raid siren went off.
Video from a local television channel aired footage of heavy fighting that had broken out in northwestern Kyiv. A Ukrainian soldier with handheld, light antitank NLAW missiles walked between burning armored vehicles and met with a fellow soldier, the video showed.
According to the Ukrainian National Nuclear Energy Supervision Bureau, a nuclear waste burial site in Kyiv was hit by Russian shells, leaving the automated nuclear radiation monitoring system damaged. The nature and severity of damage can only be determined when the gunfire ceases, the bureau said.
Russian forces from Crimea have been making large advances on cities in the south, including Mykolaiv, which is located between Odesa and Kherson. Mykolaiv Mayor Alexander Senkevich announced on Sunday morning that the city remains under Ukraine's control.
However, there had been fighting overnight. One video being shared on the Ukraine Telegram social media network showed damaged buildings and streets in Mykolaiv's center.
Ramzan Kadyrov, the leader of Russia's Chechnya region, said Chechen fighters have been deployed in Ukraine, and he urged Ukrainians to overthrow their government.
In a video posted online on Saturday, Kadyrov said Chechen units had so far suffered no losses and Russian forces could easily take large Ukrainian cities, including Kyiv, but their task was to avoid loss of life.
The Ukrainian Defense Ministry said they had found plans of Russian forces and were able to dominate them in the past 72 hours. The ministry didn't give details about Russia's plans, but confirmed the destruction of a convoy of Chechen special forces in Kyiv and the killing of a Chechen commander.
The Russian Defense Ministry hasn't responded to that statement, but did say that the 302 Anti-Aircraft Missile Regiment of the Ukrainian forces voluntarily surrendered their weapons and 471 Ukrainian servicemen have been detained.