Russian paratroopers landed in Ukraine's next largest city, Kharkiv, overnight.
Intense ground battles have been going on there against the Ukrainian army and on Wednesday morning a Russian rocket hit a police building and a university in the city.
Large Russian forces are also said to be approaching the capital Kyiv.
2,000 civilians are said to have been killed
More than 2,000 civilians have died in Ukraine in the past seven days, according to Ukraine's rescue service.
The port city of Mariupol has been surrounded by Russian forces, according to the city's mayor.
At least 100 people are said to have died in the Russian attack on the city and it must have been impossible for the injured to leave the city.
The city of Kherson in southern Ukraine is also said to be surrounded.
Russia is said to have taken control of parts of the city.
But Cherson's mayor says fighting is still going on.
"Fierce fighting and shelling continue in several cities in Ukraine, with more and more victims and humanitarian consequences," the UN coordinator OCHA wrote in a status update.
Calls resume
Both Russia and Ukraine have stated that they are prepared to resume talks held on Ukraine's border with Belarus.
So far, the talks have not led to a ceasefire and representatives of Ukraine have stated that Russia has made the same demands in the negotiations as it did before the invasion.
According to the plan, the talks will resume on Thursday.
Request protection of nuclear power plants
The Zaporizhzhia nuclear power plant has been surrounded by the Russian military, but is still under Ukrainian control.
Ukraine has requested assistance from the IAEA nuclear power agency to protect its nuclear power plant.
They also want the decommissioned Chernobyl nuclear power plant to be protected.