First Minister Arlene Foster and Deputy First Minister Martin McGuinness are among the devolved leaders stressing the need for unfettered access to the European Single Market.
The consortium of devolved leaders will make their plea at a summit meeting with UK government ministers set to be dominated by Brexit.
Ahead of the British Irish Council (BIC) summit near Cardiff, Welsh First Minister Carwyn Jones called for firm commitments on free trade.
Mr Jones, who is hosting the event, said single market access had become even more important amid the prospect of protectionist policies in a Donald Trump White House.
“This is a changing world and these are tumultuous times,” he said. “But our focus on retaining full and unfettered access to the single market is unwavering.
“Today I will once again call on the UK Government to make this their absolute priority in forthcoming Brexit negotiations.
“Let me be clear, a situation where the UK faces barriers and tariffs to trading with the European market would be disastrous for our economy and I will not support any settlement that undermines our exports.”
Mr Jones will be joined by Scottish First Minister Nicola Sturgeon, Northern Ireland’s First Minister Arlene Foster and Deputy First Minister Martin McGuinness and the premier of the Irish Republic, Taoiseach Enda Kenny, at the BIC summit.
Welsh Secretary Alun Cairns, Northern Ireland Secretary James Brokenshire and Parliamentary Under Secretary at the Department for Exiting the European Union Robin Walker will be among UK Government representatives attending.
Ahead of the event, the Scottish Government said the UK must not be “driven-off a hard Brexit cliff edge”.
External Affairs Secretary Fiona Hyslop said: “A hard Brexit outside the Single Market, is the biggest threat to the economic prosperity of Scotland and all the UK.
“Despite repeated calls from the Scottish Government and other administrations who are understandably equally concerned, the UK Government is still failing to provide any transparency on their plans with only a few weeks of 2016 left.
“There is currently no confidence in the government’s ability to fight for the benefits the single market brings, including free movement of people, and all signs appear to point to the fact they will choose to throw these away.”