The Government is expected to announce details on the operation of the Property Tax after ministers received the report of a working group that examined issues including how it will be distributed.
Former tanáiste Eamon Gilmore said before he stepped down that any changes in the operation of the tax that disadvantaged those living in the East could represent a "fundamental breach" of the agreement between the two parties.
However, Taoiseach Enda Kenny insisted that its operation would leave no local authority worse off.
The legislation underpinning the LPT allows some local authorities retain a proportion of the tax, which could allow them reduce the burden on homeowners in their area.
Some TDs has expressed concern that other grants would be clawed back in more prosperous areas of the country, and that that could limit the scope to mitigate the tax in areas like Dublin and Dun Laoghaire.
Minister for the Environment Alan Kelly will be giving details of the proposals from the group later this week.