After a second day enjoying New York, John said once back at the flat, Spacey became affectionate again and told him he felt "misunderstood".
Netflix and Media Rights Capital confirmed the news to Deadline, explaining that they have "decided to suspend production on House of Cards season six, until further notice, to give us time to review the current situation and to address any concerns of our cast and crew". Spacey also serves as an executive producer.
The young barman, who was 19 at the time, said he was sitting outside having a cigarette break when Spacey sat down next to him, flashed his privates and said: "It's big, isn't it?"
Spacey had reportedly been to a production at the Chichester Festival Theatre nearby at the time.
John told how a "charming and brotherly" Spacey showed him around the city, took him out for dinner and introduced him to famous friends on their weekend together.
The man told Victoria Derbyshire Spacey invited him to spend the weekend in NY but it became clear he was interested in "a way I wasn't".
Since the allegations from Rapp, several other people have come forward to recount similar stories.
To answer their questions, Netflix and MRC shared a joint statement with Entertainment Weekly: "MRC and Netflix have made a decision to suspend production on "House of Cards" season six, until further notice, to give us time to review the current situation and to address any concerns of our cast and crew".
A spokeswoman for the London theatre said: "During Kevin Spacey's tenure as artistic director no complaints were made against him".
The 58-year-old actor has since been stripped of an International Emmy Award and his acclaimed Netflix series House of Cards - in which Spacey stars as the manipulative, ruthless politician Frank Underwood - will end after the sixth season.
When asked about how the encounter made him feel, John responded: 'I was uncomfortable at best, traumatised at worst'.
As those closest to me know, in my life I have had relationships with both men and women.
Rapp had also said Spacey was drunk when the incident took place in 1986.
Spacey also announced that he was now living "as a gay man" but the Oscar winning actor has been widely criticised for choosing this moment to come out.
Christian Bale replaced Spacey's name in the version that aired on NBC in the United States.
Ridley Scott's "All the Money in the World", in which Spacey portrays oil tycoon J. Paul Getty, is still scheduled to premiere November 16 at the AFI Fest and hit theaters in December. Rapp, who was 14 then while Spacey was 26, claimed that Spacey harassed him at a party when he was carried "up like a groom picks up the bride over the threshold". But Sony's TriStar Pictures, which is handling the release, has not commented further on Spacey's involvement, and it's unclear whether he will do any press for the film.
He told RadarOnline.com: "I went up to order a drink and Kevin came up to me and put his arm around me".