Tánaiste and Minister for Foreign Affairs Simon Coveney has said Irish contingency plans for a no-deal Brexit will continue.
He said the politics of Brexit in Westminster are incredibly divisive and difficult, and British Prime Minister Theresa May must continue to show "the mettle" that she has demonstrated up to now.
However, she faces a major backlash from Tory Brexiteers, in addition her Brexit Secretary Dominic Raab resigned, saying he could not in "good conscience" support the deal.
Mrs May yesterday secured cabinet approval for her Brexit deal, which she described as "the best that could be negotiated".
As part of the draft agreement, Northern Ireland would stay in the same customs territory as the rest of the United Kingdom, but that the region would remain aligned to some EU regulations to avoid a hard border.
Speaking on RTÉ's Morning Ireland, Mr Coveney said Mrs May will have to persuade people that the consequences of rejecting the deal would be chaotic.
He said it was important that people do not talk down the chances of the deal getting through Westminster.
Mr Coveney said he believed that if people took the time to read the text they would realise that it is very balanced.
"I think Theresa May will now have to persuade people … that the consequences of not voting for this, of pulling it down, is chaotic, provides uncertainty for the future.
"We don't know what the political consequences of that would be. But certainly from an Irish perspective, we will continue for all eventualities, but I think it is important that people don't talk down the chances of it getting through Westminster."
His comments were echoed by Minister for Finance, Public Expenditure and Reform Paschal Donohoe, who has said preparatory work for different Brexit scenarios will continue.
However, Mr Donohoe said the Irish expectation remains the same - that the proposed deal will be passed.
Mr Donohoe said the deal respects the national priorities outlined by the Taoiseach, and that Irish officials would continue to work with EU officials to deliver those goals.
Mr Coveney said nothing is being given away on fisheries by either side in the deal and UK fish, and fish products, will not have tariff-free access to EU markets under the customs union backstop.
He said the fisheries issues will be dealt with in the negotiations on the future trading relationship and there will need to be compromise on both sides, so if the UK wants access to EU markets it will have to concede some access to its waters for EU fishing vessels.
He said, however, there are special provisions for Northern Ireland registered vessels "to ensure they can continue as normal" but in east-west trade nothing is being given away.