Taoiseach Leo Varadkar has said "more detailed and realistic proposals" are needed from the UK in relation to Brexit.
Mr Varadkar said he was concerned that some of the constraints of leaving the Customs Union and the Single Market have not been fully recognised by Theresa May's government.
He was speaking after Mrs May set out the UK's hopes for a future EU economic partnership during a speech in London on Friday.
Mr Varadkar said: "For our part, a close economic relationship is very much in the interests of Irish business, as is a smooth transition period.
"However, I remain concerned that some of the constraints of leaving the Customs Union and the Single Market are still not fully recognised."
Mr Varadkar added: "We will now need to see more detailed and realistic proposals from the UK. Brexit is due to happen in a little over 12 months, so time is short."
Tanaiste and Foreign Minister Simon Coveney said Mrs May's commitment to no hard border on the island must now be backed up by "concrete proposals".
He said that while he welcomed Mrs May's vow not to allow Brexit to jeopardise the Northern Ireland peace process, the UK must now provide the solution to how a hard border could be avoided and the Good Friday Agreement protected.
"We welcome the Prime Minister's reiteration of the UK's steadfast commitment to the Good Friday Agreement and to the commitments made in the agreement reached last December, including on avoiding a hard border.
"These commitments now need to be translated into concrete proposals on how a hard border can be avoided and the Good Friday Agreement and North-South co-operation protected."
He added: "Our shared hope is that the future EU-UK relationship can achieve these goals.
"However, we, together with the Commission, are also committed to exploring other specific solutions, if proposed by the UK."
Mr Coveney said if no solution was reached, the fall-back mechanism, as agreed in December, would entail, if necessary, "full alignment in Northern Ireland with those rules of the single market and customs union necessary to protect North-South co-operation, the all-island economy and the Good Friday Agreement, and to avoid a hard border".
Sinn Fein leader Mary Lou McDonald accused Mrs May of failing "to grasp the hard truths and realities" of Brexit.
"The hard truth is that Brexit is incompatible with the wishes of the people of the north, acts against our economy and undermines our agreements.
"The British Government knows this and that is why they have failed to bring forward any workable solutions or new thinking," she said.