Simon Coveney said the chances of agreeing to a withdrawal treaty between Britain and the European Union were good.
He told Sky News: “I think the chances are good, because I think the consequences of not getting a withdrawal treaty agreed are very very negative indeed for the UK, also for Ireland and indeed for many countries in the EU.”
Mr Coveney added that talks are now entering an intensive phase.
He said: “It is now time for the UK and EU’s talented negotiators to lock themselves into a room and complete the withdrawal agreement over the next two weeks.
“The EU summit of October 17/18 must hear of progress for a special summit to be called in November.”
He also said that the Irish position on not having a hard border has not changed.
Mr Coveney added: ”The Irish and EU position has not changed and the UK must deliver on its written commitments of last December and March.
“That is a backstop that guarantees no hard border in Ireland or related checks or infrastructure.
“We don’t want the backstop to ever be used, instead we want a close future trading relationship with the UK negotiated over the transition period of a managed Brexit.
“We believe this can be done and it is the responsibility of politicians to give the final push for a deal.”
It comes as Theresa May has only two weeks left to convince Brussels and Dublin that the UK is ready to agree to a Brexit deal, Irish taoiseach (prime minister) Leo Varadkar has warned.
Mr Varadkar said he remains hopeful that a deal can be reached but has warned there is still work to be done.
The European Commission President Jean-Claude Juncker has also said the chances of a good deal have grown, but there still needs to be work to secure this.
Diplomatic sources confirmed the European Commission president was confident of securing a good Brexit deal in the next weeks.
EU Brexit negotiators believe an agreement on the terms of Britain’s exit from the bloc is “very close”, diplomatic sources told Reuters, in a sign a compromise on a major sticking point – the future Irish border – might be in the making.
Mr Varadkar said: “There will be a summit in two weeks in Brussels that will be a time for us to take stock.
“I would be hopeful at that point that there would be decisive progress allowing us to conclude an agreement by November.
“That remains to be seen yet. I think there is a fair bit of work to be done.
“It’s increasingly important that we conclude a deal sooner rather than later.”
Mr Juncker also struck a positive note when asked if a deal could be made, told Austrian media: “I have reason to think that the rapprochement potential between both sides has increased in recent days.”