ORODYANKA/LVIV, Ukraine: Russia and Ukraine have agreed on the need to set up humanitarian corridors and a possible ceasefire around them for Ukrainian civilians fleeing the war, negotiators for both sides said following talks on Thursday.

But while Russian negotiator Vladimir Medinsky said the talks had made "substantial progress," Russian invasion forces surrounded and bombarded Ukrainian cities as the conflict entered its second week.

A Ukrainian negotiator said the talks had not yielded the results Kyiv hoped for but the two sides had reached an understanding on evacuating civilians.

In Moscow, Russian President Vladimir Putin, brushing aside worldwide condemnation of the invasion, said the military operation was going according to plan.

Ukrainian soldiers and civilians kept up their resistance to the invading force and the capital Kyiv and other main cities remained in their hands on Thursday evening.

But the humanitarian crisis deepened, with the United Nations saying one million people had now fled their homes.

Those who stayed were enduring shelling and rockets strikes on several cities, often on residential areas. Swathes of central Kharkiv, Ukraine's second city with 1.5 million people, have been blasted into rubble.

The talks, at an undisclosed location, marked the first time the two sides had agreed any form of progress on any issue since the Russian invasion.

Ukrainian presidential adviser Mykhailo Podolyak said the two sides envisaged a possible temporary ceasefire to allow for the evacuation of civilians, and the creating of humanitarian corridors to evacuate civilians.

"That is, not everywhere, but only in those places where the humanitarian corridors themselves will be located, it will be possible to cease fire for the duration of the evacuation," he said.

They had also reached an understanding on the delivery of medicines and food to the places where the fiercest fighting was taking place.

Ukrainian President Volodymyr Zelenskiy said earlier Kyiv and Moscow could find a way out of the war if the Kremlin treated Ukraine on an equal footing and came to talks with a will to negotiate in good faith.

"There are things in which some compromises must be found so that people do not die, but there are things in which there are no compromises," Zelenskiy said in a televised interview, saying he was willing to have an open conversation with Putin.

Putin remained outwardly oblivious to the almost universal global condemnation of his actions and to the international economic and financial sanctions aimed at bringing Russia's economy to its knees.

Russia's military operations in Ukraine were going according to plan, he said in televised comments, praising its soldiers as heroes.