The newspaper said the attack appeared to be part of a series of covert operations that have made officials in the United States – Ukraine’s biggest supplier of military equipment – uncomfortable.
The US assessment was based on intercepted Russian and Ukrainian communications, the paper said.
The United States intercepted Ukrainian conversations in which officials said they believed their country was responsible for the attack, and also tapped into Russian communications which indicated it was not some sort of false-flag operation by Russia, it added.
"We immediately said that the Kyiv regime was behind this," Kremlin spokesman Dmitry Peskov said when asked about the report.
"In the end, it doesn't make much difference which of the units of the Kyiv regime was behind this. The Kyiv regime was behind this, we know this, we are aware of it, and we shall proceed from this as we go forward."
US officials said they do not believe Ukrainian President Volodymyr Zelensky signs off on all covert operations, the paper said.
It is unclear to what extent he is aware of such operations in advance, the officials were quoted as saying.
Russia accused Ukraine of trying to kill Russian President Vladimir Putin in the attack. Zelensky promptly denied any Ukrainian involvement.
The Kremlin has also said the United States was behind the drone attack, a view Washington dismissed as ridiculous.