Boris Johnson has claimed any Brexit deal must involve the Irish backstop being abolished.
The new British Prime Minister today addressed the House of Commons for the first time.
He repeated his pledge the UK will leave the EU on October 31 with or without a deal.
The EU has ruled out renegotiating the withdrawal agreement but Mr Johnson insists he is determined to get a new deal.
Mr Johnson said: "No country that values its independence, and, indeed, its self-respect, could agree to a treaty which signed away our economic independence and self-government as this backstop does.
He said that he is ready to negotiate "in good faith" an alternative.
Agriculture Minister Michael Creed has said that Mr Johnson's new cabinet is concerning for Ireland.
He said that we will have to wait and see that impact the appointment of Mr Johnson as British Prime Minister will have on Brexit negotiations.
"Certainly, the makeup of his government seems to be a mirror image of his viewpoints and obviously that would be of concern to us," said Mr Creed.
The cabinet is holding its final meeting of the political term in Donegal this afternoon where talks are expected to be dominated by Brexit and events in the UK.
Business Minister Heather Humphreys said that as Mr Johnson moves into 10 Downing Street a no-deal Brexit seems more likely but reiterated that they will have to wait and see.
Taoiseach Leo Varadkar did not comment on the makeup of the new British cabinet, simply saying that he looks forward to meeting with them.