Nichola Mallon in Northern Ireland and Eamon Ryan in the Republic have agreed to progress a feasibility study.
The route would consider connectivity from Derry-Belfast-Dublin-Limerick-Cork.
Stormont Minister for Infrastructure Ms Mallon said: “Improving connectivity across our island is key in delivering better opportunities for communities, greening our infrastructure and enhancing our island-wide economy.
“I am delighted that Minister Ryan and I both share a passion for enhancing our island rail network and that we are committed to working together to achieve transformative projects that serve all of our communities.”
This study will be one of the most significant reviews of the rail network on the island in many years
It was a commitment in the New Decade, New Approach which restored Stormont power sharing this year.
Transport Minister Mr Ryan said: “While the Belfast-Dublin-Limerick Junction-Cork line is recognised as the spine of rail connectivity on the island, we need to ensure that any review of speed considers the wider network and in particular connectivity to the North-West.
“This study will be one of the most significant reviews of the rail network on the island in many years and will provide a framework to develop a much-improved rail network in the years ahead.”