"Dolphin hunting is one of Japan's traditional fishing methods and conducted properly according to law," Chief Cabinet Secretary Yoshihide Suga said at a press conference.
Suga said whales and dolphins are "important marine resources" that need to be used based on scientific data, and that it is currently up to each country to decide how to control the harvest of dolphins because they are not under the International Whaling Commission's regulation.
"We will explain our stance to the United States," he added.
His remarks came after Kennedy tweeted on Saturday, "Deeply concerned by inhumaneness of drive hunt dolphin killing. USG (the US government) opposes drive hunt fisheries."
The Sea Shepherd Conservation Society said on Friday that more than 250 bottlenose dolphins had been driven into a cove in the town of Taiji, western Japan.
Taiji, a traditional whaling town in Wakayama Prefecture, came into the spotlight through the Oscar-winning 2009 US documentary "The Cove," which depicted the slaughter of dolphins during a traditional hunt off the coast and spurred international controversy.