How to manage the land border between EU-member Ireland and British-run Northern Ireland - including an emergency "backstop" solution to prevent the return of extensive controls - remains the most contentious part of a divorce deal the contenders to become the next British prime minister want renegotiated.
In an update to its Brexit contingency plans that described the impact of a no-deal Brexit on Ireland as "profound on all levels", Dublin said it would continue to engage with the European Commission on how to keep the border open, even in a disorderly Brexit.
In a no-deal Brexit, Ireland has pledged to carry out the checks necessary to preserve its full participation in the EU's single market while avoiding any related infrastructure - aims that Prime Minister Leo Varadkar said on Monday would be "very difficult" but possible to reconcile.
"There should be no illusion - a no-deal Brexit would result in far-reaching change on the island of Ireland. This would particularly impact on North-South trade, which could no longer be as frictionless as it is today," the document said.
"We continue to work closely with the Commission with a view to minimising these negative consequences of no deal, but any arrangement will clearly be sub-optimal."
A no-deal Brexit also risks significantly undermining wider community relations and political stability in Northern Ireland, with potential related security concerns, the document said, pointing to public statements from the police that any border infrastructure or personnel would become targets for militants.
The 500 km (310 mile) frontier was marked by military checkpoints until a 1998 peace deal ended three decades of violence between Catholic nationalists seeking a united Ireland and Protestant unionists who wanted to keep Northern Ireland British. More than 3,600 people were killed in that conflict.
Additional Irish police resources have been deployed to border areas in recent months, part of a general increase in recruitment, the updated plan said, adding that further resources could, and would, be redeployed immediately in the event of a no-deal Brexit.