Russian and Ukrainian negotiators at ceasefire talks have said they have agreed to organise humanitarian corridors to evacuate civilians.
A senior Ukrainian official said that despite this outcome, the talks had not led to the results Kyiv was hoping for.
They came as Russian President Vladimir Putin defended the attack on Ukraine, saying it was “going to plan”.
But a humanitarian crisis has been growing in Ukrainian cities under intense bombardment.
Mr Putin has also spoken by phone for 90 minutes to French President Emmanuel Macron.
An aide to Mr Macron told reporters the French president expected that the worst was still to come, after Mr Putin told him Russia would continue its campaign in Ukraine until it had fulfilled its goals.
Mr Macron told his Russian counterpart the invasion was a serious mistake, and that his views did not correspond with reality.
At talks from an undisclosed location, the second this week, Russian and Ukrainian delegates agreed to possible temporary ceasefires.
But the truces would only be in places where humanitarian corridors were being set up and for the duration of civilian evacuations, Ukrainian presidential aide Mykhailo Podolyak said.
“To our great regret, we did not get the results we were counting on,” Mr Podolyak said.
Several Ukrainian cities are currently surrounded or almost surrounded by Russian forces.
The situation is particularly intense in the southern port city of Mariupol, which has been under relentless bombardment with almost no respite for several days.
Hundreds of people are feared dead in the city.
Ukraine’s second-largest city, Kharkiv, has also been under a fierce aerial assault. Its mayor told the BBC shelling and cruise missile strikes were hitting residential areas and inflicting heavy civilian casualties.
On Wednesday Russian tanks entered the port town of Kherson, a provincial capital home to about 250,000 people. It is the first major Ukrainian city to fall in more than a week of fighting. The US said the situation on the ground was changing rapidly, with fighting ongoing.
Ukraine reports that more than 2,000 civilians have died since the invasion began last Thursday. The conflict has also caused more than a million people to flee Ukraine, according to the UN.
Russia attacks Ukraine: More coverage
After his phone call with the French president, Mr Putin addressed members of his Security Council.
In televised remarks, he defended the attack on Ukraine, saying the campaign was on schedule.
He said he would never give up his conviction that Russians and Ukrainians were one people, claiming that some Ukrainians had been intimidated or “duped by Nazi propaganda”.
Mr Putin alleged that Ukrainian forces were using civilians as human shields and holding foreigners hostage. He provided no evidence for this.