Delegates from Ukraine and Russia are set to meet virtually for further talks on Monday.
A Russian delegate involved in the negotiations has said the talks have made "substantial progress" and a "joint position" could be reached soon, state-controlled Russian news agency RIA reported.
The development comes after Ukrainian negotiator, and presidential adviser, Mykhailo Podolyak also said on Sunday that he thought progress could be made in the coming days.
He added that the Russian side had become more constructive and that negotiations are "non-stop".
Again. Negotiations go non-stop in the format of video conferences. Working groups are constantly functioning. A large number of issues require constant attention. On Monday, March 14, a negotiating session will be held to sum up the preliminary results…
— Михайло Подоляк (@Podolyak_M) March 13, 2022
Nika Melkozerova is executive editor of New Voice Ukraine. She told Newstalk Breakfast there are some small positives.
"It was actually maybe a small positive sign from our president's office.
"Mykhailo Podolyak, who is the adviser to Ukraine's president head office, said that now Russians have changed the narrative a bit.
"They're no longer pressing the ultimatums - for example, that Ukraine should surrender all its territory to Russia - [and] only after that they will stop the atrocities.
"Now they are very keen on listening [to] the Ukrainian offers - that is the small positive sign we heard".
While Ukraine's President Volodymyr Zelenskyy has said "it's only a matter of time" before Russia missiles hit the homes of people in NATO countries if a no-fly zone is not set up.
He issued the warning after more than 30 Russian missiles hit a base about 20 kilometres from the Polish border - and attacks continued across the country.
Thirty-five people were killed and 134 injured in Sunday's strike in Yavoriv, which has long been used by Western experts to train Ukrainian soldiers.
Aid convoys 'legitimate targets'
It came after Russia said Western military aid convoys - which mostly come via Poland - are now considered legitimate targets.
"Nothing was happening there that could threaten the territory of the Russian Federation," said President Zelenskyy about the base attack.
"And only 20 kilometres away are NATO borders. Last year, I made a clear warning to NATO leaders that if there were no tough preventive sanctions against Russia, it would start a war. We were right."
Poland's deputy foreign minister says the attack was "highly proactive" and that Russia knows very well where the border is.
President Zelenskyy also used his Sunday message to repeat his plea for Western airpower.
"If you do not close our sky, it is only a matter of time before Russian missiles fall on your territory. NATO territory. On the homes of citizens of NATO countries," he said.
Russia's bombardment of Ukrainian cities continued over the weekend, with nine killed in bombings the southern city of Mykolaiv, according to authorities.
A monastery and children's resort were also said to have been hit by airstrikes in the eastern Donetsk region, wounding 32 people.
US journalist and filmmaker Brent Renaud was shot dead in Irpin, near Kyiv, while working for Time magazine.
A photographer who was with him was injured.
Juan Arredondo said he and Renaud were filming refugees when Russian soldiers opened fire on their car.
A statement from TIME on the death of journalist Brent Renaud https://t.co/5mXpjyl4Gd
— TIME (@TIME) March 13, 2022
In Chernihiv, northeast of the capital, heavy shelling has continued and Kyiv's air raid sirens again rang out as authorities there continue to prepare for an expected major attack.
Meanwhile 2,187 people in the besieged southern city of Mariupol have now died, according to the city council.
Drone video from the city showed the aftermath of an attack on Russian vehicles on Sunday, according to AZOV Mariupol - a unit of Ukraine's national guard which uploaded the clip.
President Zelenskyy said a humanitarian corridor to allow people to leave Mariupol had again been blocked on Sunday because of shelling - but that more than 130,000 people had escaped in six days via various escape routes in Ukraine.
Additional reporting: IRN