Irish Prime Minister Leo Varadkar hailed a Brexit agreement struck between Britain and the EU on Friday as the "end of the beginning" but said Dublin would remain "vigilant" in upcoming negotiations.
"This is not the end but it is the end of the beginning and we will remain fully engaged and vigilant through phase 2," he said, referring to the next stage of talks on post-Brexit UK-EU trade ties.
"We have achieved all that we set out to achieve in phase 1 of the negotiations. We have the assurances and guarantees we need from the United Kingdom.
"I am satisfied that sufficient progress has now been made on the Irish issues. The parameters have been set and they're good," he said, adding that there would be "no physical infrastructure" on the border between Northern Ireland and the Republic of Ireland.
Irish Foreign Minister Simon Coveney said the agreement "fully" protected the Good Friday Agreement, the 1998 peace deal which brought to an end three decades of conflict in Northern Ireland.
Coveney said the deal was a "very good outcome for everyone on the island of Ireland".
But Northern Ireland's Democratic Unionist Party, which blocked a previous version of the agreement on Monday, said it remained sceptical.
DUP leader Arlene Foster said she was "pleased" to see some changes which meant there would be no "red line" between Northern Ireland and the rest of Britain.
But she added: "There are still matters there that we would have liked to have seen clarified.... We think that we needed to go back again and talk about those matters but the prime minister has decided to go to Brussels in relation to this text," she told SkyNews.
The DUP's 10 MPs wield a disproportionate influence because they have been propping up May's government since June, when she lost her parliamentary majority in a general election.
