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"We don't believe any one, not a single beautiful phrase," Mr Zelenskyy said in a video address to the nation.
He said Russian troops were regrouping to strike in the eastern Donbas region.
"We will not give anything away. We will fight for every metre of our territory," Mr Zelenskyy said.
After another round of peace talks in Istanbul on Tuesday, a Russian negotiator said Moscow would "radically" scale back its attacks around the capital Kyiv and the northern city of Chernihiv.
But shelling continued during the night.
On Wednesday, US military officials said Russian forces began to pull out of the defunct Chernobyl nuclear power site north of Kyiv.
"We think that they are leaving. I can't tell you that they're all gone," a US defence official said.
Mr Zelenskyy said that any retreat by Russian forces was "the result of the work of our defenders".
He said that as the centre for the global fight for freedom, Ukraine had the right to demand weapons from the international community, including tanks, planes and artillery systems.
"Freedom must be armed as well as tyranny," Mr Zelenskyy said.
Meanwhile, the Russian Defence Ministry announced a local ceasefire for Thursday to allow civilians to be moved from Ukraine's port of Mariupol, which has been under siege for weeks without water, food or power.