She said it was thought the two groups could co-exist but the relationship had deteriorated.
Manager Karen Harvey-Griggs said the legal letter was "unnecessary and unfair".
"We could have co-existed harmoniously, even if they [Love Soup] wanted to set up their charity in Rotorua, but it's been made an issue and that's not fair."
However Love Soup founder Julie King said the legal action was necessary to reclaim the name.
"We asked early this year if they could stop using our name and when they continued, we decided to take legal action because the two organisations no longer have anything to do with each other."
Ms King said she intended to set up a Rotorua Love Soup kitchen in the near future.
Ms Leathers said there had been confusion between the two organisations with people making donations to the wrong group by mistake.
However Ms King said Love Soup had never received any donations intended for Rotorua Community Kai or any other charities.
Ms Leathers said her group was now looking forward.
"We are happy for Julie to roll with what she wants to do and we will continue to do our best to help hungry families in Rotorua. We are dedicated to the community and won't let anything stop us from helping those in need."