Lamya Essemlali, president of the organisation, who visits him "almost every day" in jail in Nuuk, capital of the autonomous Danish territory, told AFP he was "very clear about the situation".
"He is aware that Japan is putting all its political weight behind him, that he is a political symbol," Essemlali said.
Watson, who featured in the reality TV series "Whale Wars", founded Sea Shepherd and the Captain Paul Watson Foundation (CPWF), and is known for radical tactics including confrontations with whaling ships at sea.
The 73-year-old campaigner was arrested on July 21 when the ship John Paul DeJoria docked in Nuuk to refuel.
The vessel was on its way to "intercept" a new Japanese whaling factory vessel in the North Pacific, according to the CPWF.
Watson was arrested on the basis of a 2012 Interpol "Red Notice" after Japan accused him of causing damage to one of its whaling ships in the Antarctic two years earlier and causing injury.
Japan asked Danish authorities to extradite him at the end of July.
The Nuuk court is due to rule on his detention on August 15. A decision on the extradition is up to the Danish government.
Watson's supporters are due to demonstrate this weekend across France, before another protest in the Danish capital Copenhagen on Monday, August 12.
'No regrets'
"Even if he were guilty, it is clear that there has never been an extradition on the basis of such minor offences," Essemlali said.
"He has no regrets, he knows that what he did was right," Essemlali said, adding she had "never imagined" that Denmark would arrest Watson and consider an extradition.
Watson would be "particularly poorly treated" in a Japanese prison, she said.
In Japan, Watson faces a charge of causing injury, which can carry up to 15 years in prison or a fine of up to 500,000 yen ($3,300).
He also faces a charge of forcible obstruction of business, which carries a penalty of up to three years in prison or a fine of up to 500,000 yen.
Only Japan, Iceland and Norway allow commercial whaling.
His arrest has sparked a series of protests calling for his release.
French film legend turned animal rights activist Brigitte Bardot has campaigned for Watson in the past, and on Thursday she called for his release in a telephone interview with French television channel LCI.
"He's an extraordinary character, a hero who has spent his life defending whales against the Japanese, against the Japanese harpoons," she said.
"If he is extradited to Japan, he's dead."
French President Emmanuel Macron's office has asked Denmark not to extradite Watson, who has lived in France for the past year.
