The police force said Sunday on its official website that Russian troops opened fire on the car of Brent Renaud and another journalist in Irpin near the capital.
It said the injured journalist was being taken to a hospital in Kyiv.
A New York Times spokesperson said Renaud, 50, was a “talented filmmaker who had contributed to the New York Times over the years.”
It said he was not working for the publication at the time of his death.
The police force said “of course, the profession of journalism carries risks.”
“Nonetheless, US citizen Brent Renaud paid with his life trying to highlight the deceit, cruelty and ruthlessness of the aggressor,” it said.
Asked about the reports, White House national security adviser Jake Sullivan told CBS News that the US government would be consulting with the Ukrainians to determine how this happened and would then “execute appropriate consequences”.
“This is part and parcel of what has been a brazen aggression on the part of the Russians, where they have targeted civilians, they have targeted hospitals, they have targeted places of worship, and they have targeted journalists,” Mr Sullivan said.