The American was stopped by Britain’s Fury in Las Vegas on Saturday.
“Your king is here and I’m not going anywhere, for the war has just begun,” he said in a social media video.
“I’m a king that will never give up and will fight to the death. I am a warrior, I am strong and I will be back.”
He added: “All my love to all my people, I will see you in a few months.”
Wilder was floored twice before his corner threw the towel in during the seventh round at the MGM Grand Arena, ending his five-year reign as WBC champion, but the American said he is in “great spirits”.
Last week, in his first statement since the defeat, Wilder blamed his elaborate ring-walk costume for his performance, saying it was too heavy and he “didn’t have the legs for the fight” as a result.
Wilder also told US media he will exercise his rematch clause for a third fight against Fury.
The 34-year-old has 30 days after the fight to invoke the clause in his contract and attempt to reclaim the title from Fury, having drawn their first encounter in December 2018.