Appelbaum, a US citizen who has worked with Julian Assange and Edward Snowden, referred to the accusations as "a calculated and targeted attack" and "entirely false" in a statement published on Twitter.
But he has nonetheless left his role with the Tor Project - a software that seeks to enable anonymous communication - cryptically blaming "the way these accusations have been handled."
Late last week an anonymous website was created which collected half a dozen anonymous accounts of sexual abuse by Appelbaum, mic.com reports.
The creators of the site, which describes itself as a "collective of people who have been harassed, plagiarized, humiliated and abused - sexually, emotionally and physically - by Jacob Appelbaum", have also remained anonymous.
Appelbaum previously told The Local that he is "living in exile in Germany" because he says he has faced repeated harassment by the US government thanks to his privacy activism.
In his denial of the accusations, Appelbaum also suggests that he is the subject of a smear campaign due to his work as a free speech and secure internet advocate.
But other people linked to the Berlin hacker scene have described the sexual abuse claims as believable, reports the Süddeutsche Zeitung.
One hacker active in Berlin for several years told the newspaper: "I can feel a huge sense of relief that the silence has at last been broke."
There are also suggestions that the Tor Project forced Appelbaum out after interviews with accusers convinced them there could be substance to the claims.
On Friday afternoon, Meredith L. Patterson, a technology journalist, went so far as to openly accuse Appelbaum of rape.
"Jake finally raped enough people that Tor as an organization couldn't ignore it anymore," she tweeted.