Ukraine's military says Russian airborne troops have landed in the eastern city of Kharkiv.
"There is an ongoing fight between the invaders and the Ukrainians," the military said in a statement on messaging app Telegram.
The battle over Kharkiv intensified on Tuesday, with Russian shelling hitting residential areas and the city's central square.
Anton Gerashchenko, adviser to the Ukrainian interior minister, said a fire broke out in the barracks of a flight school in Kharkiv following an airstrike on Wednesday.
"Practically there are no areas left in Kharkiv where an artillery shell has not yet hit," he was quoted as saying in a statement on Telegram.
The country's second-largest city is home to around 1.4 million people and lies near the Russian border. It has been a target for Russian troops since last week's invasion of Ukraine began.
The city's governor said at least 21 people had been killed in shelling and 112 wounded.
Russia's Defense Ministry says Russian troops have captured the southern Ukrainian city of Kherson.
"The Russian divisions of the armed forces have taken the regional center of Kherson under full control," ministry spokesman Igor Konashenkov said in televised remarks.
The coastal city, which lies close to Crimea, has been the scene of heavy fighting in recent days.
Germany sends extra Eurofighters to NATO flank
Germany has "increased and extended" its role in NATO's enhanced Air Policing in Romania in response to Russia's invasion of Ukraine, the Defense Ministry said.
In a post on Twitter, the ministry said six German Eurofighter jets would protect the military alliance's southeastern flank until at least the end of March.
Three German Eurofighters already in Romania were joined by three additional German aircraft last week, a NATO statement said.
Enhanced Air Policing is a collective defense mission to protect and secure NATO's airspace.
Google blocks RT, Sputnik from Play store in Europe
Google says it has blocked mobile apps linked to Russian news outlets RT and Sputnik from its Play store, according to Reuters.
The step is in line with an earlier move by the company to remove the Russian state publishers from its news-related features.
The European Commission is preparing to ban Kremlin-backed media over concern they are spreading misinformation about the war in Ukraine. That has prompted several tech companies to limit distribution and advertising tools for those outlets.
RT Deputy Editor-in-Chief Anna Belkina said in a statement on Tuesday that technology companies that have cut her outlet's distribution have not pointed to any evidence that it has reported falsehoods.
Apple Inc said that RT News and Sputnik News were no longer available for download from its App Store outside Russia.
More than 450,000 refugees arrive in Poland
Poland says more than 450,000 people have entered the country from Ukraine since Russia launched its invasion on Thursday.
Deputy Interior Minister Pawel Szefernaker told private Radio Zet that the number of people crossing the border dropped slightly on Tuesday to 98,000 from a record 100,000 on Monday.
Hundreds of thousands of people have fled to neighboring countries, mainly Poland, Hungary and Romania. The UN estimates that around a million people are internally displaced, while more than four million Ukrainian refugees may need help in neighboring countries in the coming months.
