Green TD Neasa Hourigan has said she wants a new offshoot of the party to be a space that allows members to express dissent without splitting the organisation.
Ms Hourigan denied the group she helped set up - Just Transition Greens (JTG) - is a splinter group.
She said: "We're just trying to create a bit of space for people to dissent a little bit without it being a splinter. We don't need another small party on the left." The existence of the group emerged in recent days but already one of the signatories of the letter that announced it - former election candidate Saoirse McHugh - has quit JTG as well as the Green Party.
Ms McHugh left the Greens, claiming the Programme for Government is "terrible". She also said she "couldn't stomach" JTG's affiliation with the Green Party. She said she hopes it breaks off and becomes an "eco socialist party".
Ms Hourigan played down any suggestion that JTG will split from the main party, pointing out that its members went to the Greens' Executive Committee to approve the group's establishment.
She said Ms McHugh "has her own opinions about how this will play out and so do I".
Ms Hourigan was part of the Green Party's team that negotiated the Programme for Government but afterwards opposed joining a coalition with Fianna Fáil and Fine Gael.
She was overlooked for a ministerial role once the government was formed.
The Dublin Central TD said JTG will be an affiliate group like the Young Greens or Rural Greens and there are similar organisations in other European Green parties.
Asked why it was established, she said: "I don't think there's any point in pretending that the last few months haven't been difficult and there's a number of divergent views about the Programme for Government and how we should proceed."
She said that, along with Ms McHugh, other "really brilliant party activists" have taken to social media to announce they are leaving the Greens.
Ms Hourigan said "I don't want to lose those people" and said JTG could be "a generous space to start a conversation for people that don't feel they have a place for them in the party at the moment and who want to take that step back".
Ms Hourigan said she will be staying in the Green Party but said she feels "very strongly" that she doesn't want to put pressure on other people to stay.
But she added she believes there is a way for them to remain in the Green Party and contribute and she added that taking part in the JTG group would be a way to do this.