"We can avoid a hard border by signing up for the agreement that has been negotiated", said Mr Varadkar.
The so-called Northern Ireland backstop, which aims to keep the border between the British province and EU member Ireland open, would all but leave Northern Ireland inside the EU's single market if an eventual British/EU trade deal can not maintain the now frictionless frontier.
"It's a very fluid situation, and I think it'll be a very interesting day".
Northern Irish business groups lined up to back Prime Minister Theresa May's draft Brexit agreement on Friday and put pressure on her allies from the British province to drop their staunch opposition to the plan.
"Obviously if it's defeated in Westminster, it's hard to know where we go from there, as others have said it's maybe hard Brexit or no hard Brexit at all, but that's a decision for the UK Parliament to make".
"Whilst this agreement may not be ideal, and further clarification on certain aspects will be required, it is vastly preferable to a no-deal scenario and offers us an effective insurance policy in the interim period until a new trading relationship is agreed".
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"Surely we have learned lessons from the past that that is not something that would ever be in the interests of people north and south on this island", Coveney told reporters at his Fine Gael party's annual conference.
After the meeting, Sinn Fein leader for Northern Ireland Michelle O'Neill said: "We have had a very positive meeting, where we were able to seek some assurances over what has been achieved in the agreement so far".
British Prime Minister Theresa May has defiantly pledged to see her Brexit plan through, despite ministerial resignations and a plan to topple her by disgruntled Conservative lawmakers who believe the backstop arrangements around the border risk the United Kingdom staying in a customs union with the EU indefinitely.
The Brexit deal is complex and unwieldy.
"We would find ourselves after a very chaotic opening period having to agree something, having to agree something around aligning regulations and customs", he said.