"The only workable solution is for the north to be granted a special designated status within the European Union, and the Taoiseach [prime minister Kenny] needs to be working towards that goal," Sinn Fein deputy leader Mary Lou McDonald, a member of the Irish parliament, said.
Kenny said in October that Ireland would have a representative on the European Commission Brexit negotiations team.
Member of parliament Maurice Quinlivan, Sinn Fein's spokesman for jobs and enterprise, expressed concerns about Brexit's impacts on cross-border trade and free movement between Ireland and Northern Ireland.
Quinlivan stressed that the Irish government and European Union are obligated "ensure the north remains within the EU" and designated an area of special status.
May said Tuesday that the UK government was taking steps to ensure input from the country's devolved regional administrations, including the Northern Ireland Assembly, in Brexit talks.
