Ukrainian authorities say Russia is not observing a temporary ceasefire that was agreed in two cities.
The ceasefire was designed to let civilians leave Mariupol and Volnovakha.
But Ukrainian authorities say attacks are continuing, and the evacuation is postponed.
Mariupol - a key southern port - has been besieged by Russian forces for days.
Meanwhile, Vladimir Putin says he will not impose martial law - military rule - in Russia.
He also warns Western countries against imposing a no-fly zone over Ukraine.
Ukraine's president has condemned Nato for ruling out the no-fly zone.
But Western leaders say introducing the measure would be an escalation.
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