The Rev Teri Peterson, from St John’s Church, in Greenock, Inverclyde, was in the Carnival Magic’s nightclub in Miami with female members of her congregation when the incident took place.
Also present were members of RevGalBlogPals – an international online community supporting clergy women and other women in ministry.
Rev Peterson is one of the group’s office bearers.
R Kelly has been the subject of multiple accusations of sexual misconduct. Some cases have been settled out of court and the singer has been acquitted of some charges. Last month prosecutors in Atlanta and Chicago began investigating new abuse allegations.
Rev Peterson said: “On the second night of our cruise a number of the women of colour in our group were in the nightclub, dancing.
“The DJ began to play a song by R Kelly and women – not just those in our group – asked him to stop. His response was to sing and dance along and mock them.
“Later that night, elsewhere on the ship, they saw him and he proceeded to sing the song again and to mock them.
“The next time he saw them in the club – they went before his shift began and were packing up to leave when he arrived – he played and sang along to Blurred Lines while looking at them.”
The clergy group said security was called to deal with them rather than the DJ when they complained.
Rev Peterson, who spent five days emailing the company and holding meetings with onboard management, said: “The response of the management on the ship was lacklustre until the white women in our group also got involved.”
However, the women said they have not received a resolution and were unhappy at the offer of $100 onboard credit compensation.
A spokesman for Carnival Cruise Line said: “We had a small group of guests who took issue with two songs.
“While we only play radio versions of popular music sanitised so offensive language has been removed, we do not make a habit of banning music as we have a broad cross-section of guests.
“Our shipboard team listened to the concerns and provided a goodwill gesture.
“We are proud of the many ways we’ve been recognised for our commitment to diversity and inclusion … we’re sorry this group feels otherwise.”