A Fine Gael Senator has said she will be advocating a No vote in the referendum on the abolition of the Seanad.
Speaking to RTÉ's Morning Ireland, Galway Senator Fidelma Healy Eames said she was "confused" as to why Taoiseach Enda Kenny wants to get rid of the upper house.
Ms Healy Eames said that although she supports the idea of holding a referendum, she would not be supporting her party's position.
Speaking on the same programme, Labour Senator Susan O'Keeffe said she also disagrees with her party's position on the future of the Seanad.
Senator O'Keeffe said she "applauded and welcomed" the opportunity to discuss the future of the Seanad, while she also confirmed that she will vote in favour of the legislation to bring about a referendum on the upper house.
However, she said she would not be taking an active part in the referendum campaign.
"For myself, I believe the Seanad should be retained and reformed. I won't be running around if you like campaigning for that.
"I think there will be many more people making that argument," she said.
The Taoiseach has warned he expects all politicians in the Government to back the referendum to abolish the Seanad.
Mr Kenny said: "It is a Government position, it is a Government decision and it is a Government programme.
The Government this week published its proposed amendment to the Constitution to abolish the Seanad.
The 32nd Amendment of the Constitution (Abolition of Seanad Éireann) Bill 2013 provides for 40 amendments to the Constitution to remove references to the Seanad.
If passed by the people in a referendum, the Seanad would cease to exist from the time of the next General Election.
Yeats comments not about Seanad debate - Higgins
President Michael D Higgins has said comments he made in Croatia about Senator WB Yeats were not in any way related to the planned referendum on Seanad abolition.
He said the reference was appropriate because the poet had signed a letter to a Croatian sculptor as Senator WB Yeats.
Sculptor Ivan Mestrovic had applied to design the currency of the new Irish State in the 1920s.
Ahead of an Irish music concert in Zagreb yesterday, President Higgins made reference to two speeches WB Yeats made in the Seanad in the 1920s.
He had earlier described Yeats as a great poet and Senator.
However, President Higgins said it would be wrong to view his comments as a contribution to the current debate on the Seanad.
He said the future of political institutions is a matter for Government and the people.