Plans include business networking, school visits, liaising with student groups, and simply socialising. It has a social media presence, and is working on setting up a website.
Ms Marks, who founded the Mitzvah Day social action project, and was made an OBE for her interfaith work this year, says women have an advantage when it comes to fostering relations across the religious divide.
She said: "We tend to be more collaborative, we tend to be less competitive, we tend to be more practical - traditionally that's just what women are like, particularly Jewish and Muslim women.
"We thought we might be able to make some headway by approaching it differently as women."
The idea for the group stemmed from a discussion in March 2014 between Prime Minister David Cameron and Baroness Warsi, at the time minister for faith and communities.
Ms Marks recalled: "I was talking about interfaith and integration. Baroness Warsi said she wanted to help set something up which was Muslim, Jewish and women."
But Ms Marks acknowledged that some people in both communities would not see the need for such a group. "But the climate we are all living in means that it is crucial we bring these two communities together," she argued.
Mrs Siddiqi, who was inspired by Mitzvah Day to set up its Muslim counterpart Sadaqa Day, said she felt that "not enough effort has been done before" to bring the communities together.
She said: "The right people haven't been involved. Perhaps the focus has not been there. When anything happens abroad, like it did last summer [during the Gaza war] or the killings in France, it has a huge impact on us all here in the UK as well.
"The kinds of friendships and bonds of trust that this work is fostering and encouraging will ensure that women - and also men where appropriate - will be able to work through such times with respect and resilience. When people develop respect through friendship, communities most certainly become stronger."
She added: "Women have a unique and central role in all of this but have not been included enough in the past. Nisa-Nashim is changing that and it is working very well.
"There is something special and different in a room of just women - especially the kind of switched-on, motivated and dynamic women that Nisa-Nashim seems to be attracting."
