Negotiators from Ukraine and Russia convened for a third round of talks on Monday, with the Ukrainian delegation saying there was potential progress on ensuring humanitarian corridors.
Although an overall deal has not been reached, Ukraine's lead negotiator, Mykhailo Podolyak, said on Twitter after the talks that "there were some small positive shifts regarding logistics of humanitarian corridors."
Podolyak did not elaborate on any details, but Russia's lead negotiator, Vladimir Medinsky, said he expects the humanitarian corridors will start functioning Tuesday.
On the potential for a political settlement on securing a cease-fire, Medinsky said that Russia's "expectations from the talks have failed." He added that he expects more talks to take place.
"We hope that we will be able to make a more significant step forward next time,'' he told Russian media.
Both Russian and Ukrainian delegations arrived on Monday at the meeting place close to the border with Poland, the same site as the previous round of talks.
The previous meetings failed to end the conflict, with each side blaming the other for the failure to find a suitable agreement. Russia has blamed Kyiv for the previous failures to implement the cease-fire.
What happened in previous Ukraine-Russia talks?
The second round of talks, which took place last Thursday, ended with the two sides agreeing to set up humanitarian corridors for the evacuation of civilians in cities under siege.
But attempts on both Saturday and Sunday to maintain a cease-fire in several cities lasted only hours and left thousands still trapped without access to food, water or electricity.
Ukraine rejected a third attempt on Monday, ahead of the talks, after Moscow offered safe passage from several cities that would take the civilians into Russia.
The first round of talks took place inside Ukraine, close to the border with Belarus. Ukrainian negotiators had rejected Moscow's proposal to meet in Belarus, a close Russian ally that has allowed Russian troops to use its territory as a launchpad for invading Ukraine. Subsequent negotiations have taken place in Belarus, close to the Polish border.