The country faces a shortage of troops in the campaign against Russia's better equipped and larger military
Separately, the Interfax Ukraine agency said Russian soldiers were trying to capture one of the city's electricity generating stations.
Hours earlier, Ukrainian President Volodymyr Zelenskiy had predicted Russian troops would mount an assault overnight.
"Military criminals of Russia attacked one of the military units in Kiev on Victory Avenue. The attack has been fought back," the armed forces of Ukraine said in an English-language posting on Facebook.
It gave no details and the report could not immediately be confirmed. Peremohy, or Victory, Avenue is located just to the west of the centre of Kyiv.