Major cities – including Kyiv, Kharkiv, and Chernihiv – remain under attack from Russian forces.
A government official said dozens of civilians were killed in Kharkiv as shelling continued into the morning.
On the northern border with Belarus, Ukrainian and Russian officials are meeting for talks for the first time.
Hopes for a breakthrough are slim – but Ukrainian President Volodymyr Zelensky said there was a “small chance to end the war”.
The United Nations human rights chief, Michelle Bachelet, said millions of civilians were being forced to huddle in makeshift bomb shelters such as underground rail stations to escape explosions.
Since the invasion began on Thursday, her office has recorded 102 civilian deaths, including seven children – and more than 300 injured.
“The real figures are, I fear, considerably higher,” she said.
In the capital, Kyiv, the bulk of Russian forces is about 30km (19 miles) outside the north of the city, slowed by fierce Ukrainian resistance, according to the UK Ministry of Defence.
But street-level fighting continues in several parts of the city. Despite the danger, a two-day curfew has been lifted, with residents emerging from underground shelters to buy food and gather supplies.
Kasenya, who spent more than 36 hours underground, told the BBC she had managed to get home. “I can’t describe how I am feeling, I’m happy to stay alive and safe and just have the possibility to see my splendid and beautiful Kyiv,” she said.
“Even underground, everyone is trying to help one another and help our army to be stronger and to spread the world about our situation here.”
To the north and northeast, Kharkiv and Chernihiv were also shelled by Russian forces overnight but remain in Ukraine’s control. Shells landed near a shopping centre in Kharkiv during the day, while fighting continued in the streets.
Anton Herashchenko, an adviser to the interior minister, posted to Facebook: “Kharkiv has just come under massive shelling from Grads [multiple rocket launchers]. Dozens have been killed and hundreds wounded!”
To the south, Russian forces are trying to take control of the key strategic port of Mariupol, near Russia-annexed Crimea. Ukraine denied reports that Zaporizhzhia, home to Europe’s largest nuclear power plant, had fallen into Russia’s hands.