The paper rejects a call for the UK to remain in the EU customs union
The Foreign Affairs Minister Simon Coveney says there is still a lack of detail on what the Irish border will look like post-Brexit.
It comes after a UK policy paper that says they want a frictionless border between the Republic and the North.
London says it wants no border posts or physical monitoring installed at the border.
The position paper has effectively recommended no change to the current arrangements.
It also says London is committed to maintaining the border-free Common Travel Area covering Ireland and the UK.
That means free movement across the border for Irish, British and EU citizens.
The British government said it wanted a seamless and frictionless frontier without "physical border infrastructure and border posts".
"We don't want to see a border between parts of the United Kingdom," Prime Minister Theresa May said.
"What we want to see is an arrangement in relation to customs and borders with the European Union which will enable us to see no return to the hard borders of the past in Northern Ireland, to enable that flow of goods and people between Northern Ireland and the Republic of Ireland.
"That's not just in the interests of Northern Ireland and the UK, it's in the interests of the Republic of Ireland and the European Union too. "
The paper recommends CCTV cameras or number plate recognition systems as part of a frictionless border.
But it rejects Taoiseach Leo Varadkar's call for the UK to remain in the EU customs union - and instead calls for a new post-Brexit customs arrangement.
The paper rejects the idea of moving the border into the Irish Sea - a suggestion floated by Minister Coveney following the completion of the last round of negotiations in July.
It claims the idea is "not constitutionally or economically viable."
The Irish Government says it welcomes the position paper, adding: "The emphasis on the priority areas identified by the Government, including the Common Travel Area, the Good Friday Agreement, North/South cooperation and avoiding a hard border, is welcome.
"Protecting the Peace Process is crucial and it must not become a bargaining chip in the negotiations.
"The Government will analyse the paper in detail, along with the UK paper published yesterday on Future Customs Arrangements."
The Government says it will also engage closely with the European Commission, the Barnier Task Force and our EU27 partner member states.
Some 30,000 people cross the 500 kilometre border every day without customs or immigration checks.
The paper also says the UK government wants the Good Friday Agreement to be written into EU withdrawal agreement.
The document is the second in a series of position papers about Brexit.
On Tuesday, London published its plans for a temporary customs union with the European Union, drawing a cold response from Brussels.
The European Commission tweeted: "UK's papers, a positive step towards really starting phase 1 of negotiations. Clock is ticking & this will allow us to make progress".
It also said: "On Ireland, we must discuss how to maintain Common Travel Area&protect Good Friday Agreement before looking at technical solutions."
#Brexit -On Ireland, we must discuss how to maintain Common Travel Area&protect Good Friday Agreement before looking at technical solutions— European Commission (@EU_Commission) August 16, 2017
But Minister Coveney says some of the proposals will not work.
"There are all sorts of problems with that, that I think we understand very well on the island of Ireland in the context of smuggling and so on.
"And certainly from an agri-food point of view, how that could be possible I just don't see how it could work.
"If you look at the diary industry for example; milk powders go into yogurts, cheeses, butters, liquid milk and they end up across multiple markets".
Read the documents in full here
Additional reporting: Jack Quann