Kyiv Mayor Vitali Klitschko says the city is not surrounded on all sides by Russian forces but that the situation remains very tense.
"Kyiv is not completely surrounded. The Ukrainian army is fighting hard in the outskirts and the Russian army has many casualties," he told the German tabloid Bild.
Klitschko wrote separately on Telegram that there was misinformation being spread about the positions of Russian soldiers.
Air raid sirens were heard in the city on Sunday evening.
A curfew was in force from 5 pm to 7 am.
