Russian President Vladimir Putin proposed direct talks with Ukraine just over an hour after his ceasefire ended, something Zelenskiy said was possible, but only after Moscow agreed to an unconditional 30-day ceasefire from Monday.
The commander of a drone unit in Ukraine's national guard told Reuters any talks could only start with a full Russian withdrawal to Ukraine's borders when the country won independence in 1991.
"As a soldier and a citizen of Ukraine, I believe that before we sit down at the negotiation table, we should go back to the borders of 1991," the commander known as Chepa said in a bunker near the front line.
"That's it. Full withdrawal of all troops from the territory of Ukraine. Then when we can talk. Whatever he (Putin) is thinking of, take certain regions or divide territories, nobody has given him the right to do it."
Chepa's views were echoed by others in the unit.
Russia occupies nearly a fifth of Ukrainian territory and has repeatedly said Kyiv must recognise the "reality on the ground".
Zelenskiy has acknowledged that at least some of Ukraine's occupied territory will have to be retaken through diplomacy.
But Kyiv cannot legally recognise Russian control over any Ukrainian territory because of the constitution.
Zelenskiy has said any discussion about territory can only take place after a ceasefire is in place.
Putin used a late-night press conference to make his proposal for talks, which he said should be based on a draft deal negotiated in 2022, under which Ukraine would agree to permanent neutrality.
That would contradict Ukraine's constitution, amended in 2019 to include the goal of fully-fledged membership of NATO.
Zelenskiy received a show of support from European powers on Saturday, when the leaders of Britain, France, Germany and Poland backed an unconditional ceasefire beginning on Monday.
Chepa said he also wanted negotiations but feared they would never come about.
"Yes, we do need negotiations. But he (Putin) is scared of talks," Chepa said, adding his brigade had seen no evidence of a ceasefire over the weekend.
"We have not seen any ceasefire, there were continuous attacks by howitzers, rocket launchers, they used it all. We have not experienced any ceasefire."
The Russian movements continued into Sunday, after the Russian-declared ceasefire ran out when the reconnaissance drones flew over a nearby village.
"There is a lot of movement there of military as well as civilian vehicles," Chepa said.
