Marcella Corcoran Kennedy, the junior health minister, said she will consider possible solutions after meeting backbench TDs last night.
Under Government plans, shops are set to be told they cannot sell alcohol alongside other products and must limit the sales and promotion to areas separate to where other products are sold. The move is part of wider attempts to reduce the negative impact of alcohol.
Ms Corcoran Kennedy gave a presentation to Fine Gael TDs at their weekly parliamentary party meeting last night.
During more than 90 minutes of debate, at least 15 TDs said while they support the measure, there are concerns about its impact on smaller shops that may lose customers to unaffected off-licenses.
Ms Corcoran Kennedy was strongly supported by Taoiseach Enda Kenny and Tánaiste Frances Fitzgerald.
Ms Corcoran Kennedy said she is open to finding a solution to concerns, including the possibility of exemptions for corner shops and other potential moves.