The city's mayor said Ukrainian forces have pushed back Russian forces in several areas near Kyiv, vowing to defend all buildings rather than give up the capital.
Ukrainian forces already control the small city of Makarov and most of Irpin, according to Kyiv mayor Vitali Klitschko.
In the east, Irpin borders Kyiv, and in the west, Makariv is about 50 kilometres (30 miles) away.
Irpin and Lyutizh, both north of Kiev, experienced fierce exchanges of artillery fire, with considerable activity behind the front lines in Irpin, AFP journalists reported.
Several Ukrainian news agencies reported Russian troops may surround the western suburbs of Kyiv, including Irpin, Bucha, and Hostomel.
Litschko stated that he didn't have any additional information about Ukrainian counteroffensives.
On February 24, Russian troops invaded the country, pushing quickly to the outskirts of Kiev, but have been unable to encircle the city and enter it.
Former boxing champion Klitschko said the capital of Ukraine is the target of aggressors "because the city is the heart of the country."
Ukrainians are ready to defend Kiev building by building, he said, urging Russian soldiers to return home.
"We would rather die than kneel in front of the Russians or surrender to the invaders," said Klitschko.
"We are ready to fight for each building, each street, every part of our city."
Several buildings were damaged in a residential area of northwest Kyiv on Wednesday morning, while four people were injured.
Four people were injured in a building explosion in a residential area of northwest Kyiv on Wednesday morning.
73 civilians, including four children, have died in the capital since the invasion began. Another 297 have been wounded.
Curfews have been in place in Kyiv since the beginning of the week, according to Klitschko. The president explained that the curfew was necessary due to military information about possible attacks.
He said dozens of saboteurs had been arrested since the start of the conflict.