Russian troops now control a narrow path across the Dnieper river into the east of Kyiv, according to the Institute for the Study of War.
Overnight there were reports of clashes with so-called saboteur groups on the city streets - and an oil depot was hit at Vasylkiv south of the city.
A residential block in the suburb of Bucha was hit by shelling, and there was heavy fighting in nearby Irpin.
On Saturday there were explosions in the west of the city near Peremohy Avenue and a residential apartment building was hit by a missile.
There has also been fierce fighting at Hostomel airport, to the west of Kyiv.
Russian troops around Ukraine
Russia is now in full control of significant parts of Ukraine's territory.
After Ukraine's air defences and other military infrastructure came under attack on Thursday, columns of tanks moved into position, backed up by artillery and air power.
