Missile strikes killed dozens of civilians in the country's second city, Kharkiv, while air raid sirens sounded again in the capital, Kyiv.
Ukraine's President Volodymyr Zelensky called the Russian bombardment of Kharkiv a "war crime".
There were reports of fierce shelling in the northern city of Chernihiv.
Russia is attacking Ukraine on several fronts, but its advance has been slowed by Ukrainian resistance.
All three cities remain under Ukrainian control.
Away from the battlefields, economic and diplomatic moves have continued.
President Vladimir Putin has banned Russians from moving money abroad as he tries to halt a plunge in the value of the rouble following the imposition of sanctions.
And a rare emergency session of the United Nations General Assembly has heard a demand from the secretary general for an immediate halt to hostilities.
On the northern border with Belarus, Ukrainian and Russian officials ended their first round of talks.
There was little expectation the session would bring a breakthrough, but a Ukrainian official said both sides would now return to their respective capitals for further consultations before a second round of negotiations.
Russia said both sides had agreed to continue talking and would meet again "in the next few days".
New members have been joining the Territorial Defence Forces in Kyiv. IMAGE SOURCE,REUTERS
In a late-night address, Mr Zelensky said there were eyewitness accounts of civilians being deliberately targeted during a sustained attack on Kharkiv.
He called for the West to consider a no-fly zone over Ukraine - something the US so far ruled out over fears it could draw it into a direct conflict with Russia.
Videos shared on social media showed rockets landing in Kharkiv, in what some defence analysts described as typical of a cluster munition strike on a dense urban area.
Russia has previously denied targeting residential areas.
New satellite images showed a Russian military convoy stretching for about 40 miles (64km) north of Kyiv.
But reports of fresh fighting on the outskirts of the capital forced residents back into their shelters on Monday evening.
Another video circulating on social media showed huge clouds of smoke at a burning shopping centre in Chernihiv, another city that has been under pressure from the Russian offensive.
One teacher in Chernihiv, Oksana Buryak, told the BBC the situation was "like from some horror movie".
"Our hearts are broken, we don't understand anything," she said.
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 hands.
Ukrainian Interior Minister Denys Monastyrskyy, speaking to the BBC, said the situation across the country was "serious, but stable".
"Every day the enemy sends more and more forces. But our glorious armed forces are basically destroying everything that arrives to Kyiv," he added.
The UN 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.
-- Courtesy of BBC News