Ukrainian President Volodymyr Zelensky on Sunday renewed his plea for talks with his Russian counterpart, taking to US television to say negotiations were the only way to "end this war."

He stressed that he and President Vladimir Putin were the only principals able to thrash out a deal to stop the fighting, now in its fourth week.

But he signaled he would lay down red lines against ceding Ukrainian territory, including two pro-Moscow breakaway regions.

"I'm ready for negotiations with him," Zelensky told CNN show "Fareed Zakaria GPS."

"I think without negotiations we cannot end this war," the Ukrainian leader said through a translator.

The reiteration of Zelensky's call for peace talks came as he and other Ukrainians accused Russia of committing war crimes after authorities said the invading forces had bombed a school sheltering some 400 people in the besieged city of Mariupol.

"Russian forces have come to exterminate us, to kill us," said Zelensky.

The leader, who has emerged as a national hero for his very public stance against Putin and his forces, has spoken of Ukrainians' fierce resistance to the invasion and told Russia that several thousand of its soldiers have died in battle so far.

In this handout picture taken March 20, 2022 and released by the Ukrainian Presidency Press Office, Ukrainian President Volodymyr Zelensky delivers a video address in Kyiv
In this handout picture taken March 20, 2022 and released by the Ukrainian Presidency Press Office, Ukrainian President Volodymyr Zelensky delivers a video address in Kyiv UKRAINIAN PRESIDENTIAL PRESS SERVICE via AFP / Handout

"If there is just one percent chance for us to stop this war, I think that we need to take this chance... to have the possibility of negotiating, the possibility of talking to Putin," he said.

"Dialogue is the only way out," and "I think it's just the two of us, me and Putin, who can make an agreement on this," Zelensky said.

"If these attempts fail, that would mean that this is a third world war."

Zelensky repeatedly has warned of the potential for the Russia-Ukraine conflict to mushroom into an all-out global war.

Last month, in a move seen as precipitating the conflict, Putin recognized two breakaway regions of eastern Ukraine, Donetsk and Lugansk, as independent entities, and debate has simmered about whether Zelensky might concede the regions as a way to bring the war to a close.

But on Sunday Zelensky stood defiant: "You cannot just demand from Ukraine to recognize some territories as independent republics," he told CNN.

"These compromises are simply wrong," he added. "We have to come up with a model where Ukraine will not lose its sovereignty, it's territorial integrity."

The crisis in Ukraine, in which Putin has sought to eradicate pro-Western leanings in the ex-Soviet state, has already triggered the largest refugee crisis in Europe since World War II.