The group will comprise key bodies associated with preparing a successful bid and it will report back to both Governments in a few months for agreement on moving forward to prepare a formal bid for the 2023 World Cup.
Minister Leo Varadkar said: "Minister Ring and I were delighted to meet with Ministers Foster and Ní Chuilín to discuss the possibility of making a formal bid for the 2023 Rugby World Cup.
"It was a very useful meeting and we have now agreed to set up a working group to draw up the road map for our bid. It's still very early days, but the four of us believe that Ireland has what it takes to host a cracking World Cup."
Minister Michael Ring commented: "An event of this scale will not only have a great benefit for rugby but will also raise the profile of what sport can do for the country. We all witnessed the massive boost to the national mood that was provided by the London Olympics.
"The Rugby World Cup is probably the largest event we could ever host on our own on the island and I would hope it would have a similar impact here.
"Sport is a great unifier, it brings people together and large events like this can also bring about a great sense of pride."
Northern Ireland's Minister for Culture, Arts and Leisure, Carál Ní Chuilín, said: "The island of Ireland has a lot to offer the global rugby family and there would be a lot of benefits to be gained by hosting such a prestigious event.
"The Executive is investing £110m in upgrading stadia in Belfast which includes the redevelopment of Ravenhill.
"While we would have world class venues to host the Rugby World Cup, there is a lot of work required to get us into a position to make a successful bid."
Northern Ireland's Enterprise, Trade and Investment Minister, Arlene Foster, added: "Attracting major international events is a key element of the Northern Ireland's Programme for Government. As we already know, sport is an incredibly powerful sales tool that has the power to attract thousands of international visitors.
"Northern Ireland hosted the hugely successful Irish Open in 2012 and this year, 'La Grande Partenza' or Big Start of the Giro d'Italia will take place in May.
"Hosting events such as this provides us with a tremendous opportunity to grow tourism, boost visitor spend, and stimulate the continued growth of the Northern Ireland economy."
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