Previously, Maija Lazdiņa, the spokeswoman for RMS, told TVNET that kisses will be accepted as payment only for heterosexual couples.
The spokeswoman said that the initiative is only meant to support relationships established as traditional.
Mozaika insists that the free rides are illegal due to discriminating people over their sexual orientation and gender, referring to articles 8 and 14 of the European Convention on Human Rights.
The group also referred to Latvia's Consumer Protection Law, saying that as there are more men than women in Latvia, women are also ill-treated with the 'free rides for couples' initiative.
"Examples like this, when discrimination can be seen with the naked eye in the society are no longer to be ignored," said the head of Mozaīka Kristīne Garina.
RMS is the sub-contractor of the Rīgas Satiksme municipal public transportation company. RMS has been servicing Riga's minibus routes since 2013.