There has been heavy fighting early on Monday in a broad area from the north to the west of Kyiv, according to Ukrainian officials and social media content.
Russian forces appear to have gone on the offensive in several areas to push towards the Ukrainian capital.
With extreme rage, the enemy destroys Bucha, Hostomel, Vorzel, Irpin. They deliberately kill civilians," said Kyiv Mayor Vitaly Klitschko.
Multiple reports speak of heavy fire in all four districts on Monday as civilians continue to flee the fighting.
"We are doing everything in the capital to support the city, to create a reserve of food, medicines, essential goods. We distribute and provide aid to those who need it the most today. Humanitarian aid was also sent to Chernihiv [a city north of Kyiv]," Klitschko added.
"We are trying to deliver it to Bucha and Hostomel. We are forming humanitarian cargoes for some other cities. The capital is preparing for defense. I ask all Kyiv residents to keep calm, to stay at home, or -- in case of alarm -- in shelters."
The mayor of Hostomel, Yuriy Prylypko, was killed while "handing out bread to the hungry and medicine to the sick, comforting the desperate," according to the town's Facebook page. Two others with him were also killed.