Concerts by Capleton have been cancelled in France after protests by a gay rights group.
Six music venues axed scheduled performances in response, but others are still going ahead.
Other gay rights groups stopped short of calling for an outright ban, saying that such a step might do more harm than good.
Hate laws
Actions Gay LGBT association, based in the north-west France, said: "It will just increase the level of hate."
But the group added it was seeking written assurances from the singer that he will not use homophobic lyrics, and want performances halted if he does.
France has strict laws banning public hate speech and defamation.
Capleton still has several concert dates scheduled in France during June, including one at Le Zenith, in Paris, on 26 June.
Daniel Colling, Zenith's director, said: "My responsibility is to react if an artist makes illegal comments on stage.
"At the same time, I am bothered by the idea of judging and condemning someone before the act."
Offensive songs
But Colling did say the event would be cancelled if Capleton refused to sign a document pledging not to use defamatory speech during his performance.
Capleton was one of eight reggae singers whose record labels and promoters struck a verbal deal with the UK-based the Stop Murder Music coalition earlier this year.
They pledged not to release or re-release any offensive songs and make stars agree not to perform such tunes on stage.
But the artists themselves were not involved in the negotiations and have not directly signed up.
