The US project will follow a modern day Sherlock Holmes (Jonny Lee Miller) as he solves crimes in contemporary New York, in a format similar to the Cumberbatch BBC drama.
"As we already know with the Downey Jr movie franchise that there's room enough for two [Sherlock Holmes projects], so why not three?" the actor said at a Q&A session in New York to promote Sherlock series two airing on PBS.
Cumberbatch added that he considers Trainspotting star Miller - with whom he starred in the play Frankenstein at the National Theatre - a "friend".
"[Elementary will] be different and I don't think it'll take away the love for ours, and there's no reason to be churlish or bitter about them or what they're trying to do," he said.
In March, Sherlock co-creator Steven Moffat revealed that CBS had been denied permission to remake the show, before embarking on its own Conan Doyle adaptation.
A third series of Sherlock is expected to begin filming in early 2013, while Elementary is a strong contender for the CBS 2012-13 television season.
> Sherlock series three details revealed by Mark Gatiss
Photo gallery - 'Elementary' pilot shoot in New York: