The Reform Alliance was formed last year by five former Fine Gael TDs (members of parliament) and two former Fine Gael senators.
The group has denied speculation that the public meeting in Dublin was about the formation of a new political party.
They said it was a "listening exercise" about the future of the Republic.
The group of seven includes Lucinda Creighton, who lost her ministerial post after defying the party leadership over the abortion bill.
She was expelled from the Fine Gael parliamentary party last July, after voting against the government as the Irish parliament passed legislation allowing abortion in limited circumstances.
Speaking at the meeting in Dublin, Ms Creighton said the work of the Reform Alliance was not about party politics or replicating what already exists in Irish politics.
She said its purpose was to get those in power to embrace reforms in politics, the economy and the Irish health sector.
Ms Creighton was given a standing ovation when she mentioned the stand she and her Reform Alliance colleagues took against abortion legislation.
The group now plans to hold further meeting around the Republic.
A crowd of 1,000 people have attended a meeting held by a group of seven Irish politicians who were expelled from the Fine Gael party over abortion reform.