Ukrainian media say that Sergei Yevsyukov, 49, was killed in a blast from an explosive device planted under his car, with one outlet reporting that the explosive was equivalent to about 100g of TNT.
The Republican presidential nominee has repeatedly criticised the Ukrainian leader on the US campaign trail, and a meeting between the pair had seemed unlikely until hours before.
Speaking to US broadcaster ABC News, Zelensky also said that the victory plan he will present to US President Joe Biden this week will require Ukraine's allies to "strengthen" the Ukrainian army.
Zelensky's visit to the US coincides with efforts from the White House to prepare a new $375m military aid package for Ukraine.
In a dramatic move, an International Chess Federation (Fide) general assembly meeting in Budapest voted to maintain sanctions against Russia and its ally, Belarus.
The Ukrainian president said he would not give the number of wounded as that would help Russian military planning.
