In August, the U.S. National Marine Fisheries Service -- a division of the National Oceanographic and Atmospheric Administration --rejected the aquarium's application to import the whales.
The federal fisheries agency cited concerns five of the animals may have been still nursing when captured in Russia's Sea of Okhotsk between 2006 and 2011, and said granting the aquarium's request could negatively impact the local whale population.
In response, the aquarium filed a lawsuit in the U.S. District Court for the Northern District of Georgia.
"We could walk away. But we're not prepared to do that, because we all believe so deeply and we're so committed to this project," Scott Higley, a spokesman for the aquarium, told the Environment & Energy Publishing website.
The fisheries service, which has 60 days from the filing date to respond, declined to comment, the website reported.
The whales are currently being held at the Utrish Marine Mammal Research Station in Russia.