"People were running for cover amid sounds of explosions and machine gun fire," AFP reported.
The loudest explosion was heard in the center of town as pictures began emerging of Russian military vehicles on city roads.
The report says gunfire was heard in the city center near the government quarter.
Ukraine's defense ministry called on residents to resist the Russian forces.
"We call on all residents to inform us of Russian troop movements, prepare fire bombs and stop the enemy," a ministry statement said.
Officials said two Ukrainian military vehicles were captured by invading forces who then headed to the center of Kyiv disguised as local military, foreign media reported.
The recent fighting came as Russian forces attacked numerous targets around the country.
A senior government source in Kyiv said Friday may end up being the most serious day of fighting.
The city was under repeated missile fire from the early hours on Friday as residents were urged to take cover underground.
"Horrific Russian rocket strikes on Kyiv," Foreign Minister Dmytro Kuleba wrote on Twitter. "Last time our capital experienced anything like this was in 1941 when it was attacked by Nazi Germany.
Anton Herashchenko, an adviser to the interior minister said that Ukrainian forces downed an enemy aircraft over Kyiv in the early hours of the morning.
The aircraft crashed into a residential building and set it on fire, injuring at least eight. It was unclear whether the aircraft was manned or whether it could be a missile.
A series of explosions were heard in Kyiv earlier, which Herashchenko said were the sounds of air defenses firing at the aircraft. Further explosions could be heard just before dawn, a witness said.
A senior Ukrainian official said Russian forces would enter areas just outside the capital, Kyiv, later on Friday and that Ukrainian troops were defending positions on four fronts despite being outnumbered.
Russia launched a full-scale invasion of Ukraine on Thursday and Kyiv has reported at least 137 deaths and hundreds of wounded.
An estimated 100,000 people fled as explosions and gunfire rocked major cities. Dozens have been reported killed.
Authorities said intense fighting was under way on Friday morning in the city of Sumy in the country's northeast, while a border post in the southeastern Zaporizhzhya region had been hit by missiles, causing deaths and injuries among border guards.
Ukrainian President Volodymyr Zelenskiy said on Friday that he was named by Russia as their number one target adding that continued Russian aggression against his country showed that sanctions imposed on Moscow by the West were not enough.
Zelenskiy said the world was continuing to observe what was going on in Ukraine.
Addressing the Russian population in Russian at the end of a televised speech, Zelenskiy said the bombing of Kyiv was reminiscent of Nazi Germany's attacks during World War Two.
"This is reminiscent of 1941," Zelenskiy said.
