It wants the Northern Ireland power-sharing executive to agree a joint initiative that would curb cut-price alcohol sales in the two jurisdictions and ban retail outlets from using drink as a loss leader to attract customers.
The Republic has already reduced the hours during which stores and off-licences may sell alcohol and outlawed bogof promotions.
The measures, aimed at reducing binge-drinking and combating street violence, have had limited success and justice minister Dermot Ahern is proposing a stricter regime. The Irish Competition Authority has joined the debate, suggesting that raising prices, rather than curbing discounts, would be more effective.
The dilemma for the Government is that any price increase will add to the exodus of shoppers to Northern Ireland, where they can buy drink more cheaply thanks to the lower VAT rate and the fall in sterling against the euro.
Ahern has written to his counterpart in the Northern Ireland Assembly, social development minister Margaret Ritchie, suggesting an all-Ireland approach.
In his letter, the minister said the proposed joint initiative would target "the volume-based promotions that are designed to increase the quantities of drink sold and, in some cases, result in excessive consumption of drink and in alcohol-related harm".
He added: "I am conscious that the effectiveness of any actions taken here in the Republic to curb such promotions could be reduced if similar action is not taken on an all-island basis. It would be desirable to have a common approach in dealing with this problem."
In February The Grocer also predicted Northern Ireland could become a destination for Scottish shoppers seeking cheap booze if legislation to curb binge-drinking was brought in by the Scottish Parliament.