Theresa May is facing a fresh Brexit challenge amid reports that Dublin wants the Irish Sea to be the country's border with the UK.
Ireland's new Taoiseach Leo Varadkar is unconvinced by the UK's plans to introduce a high-tech land border between Northern Ireland and the Republic after Brexit, according to The Times.
It comes after Home Secretary Amber Rudd pledged there would be "no cliff-edge" on freedom of movement after Brexit, as she outlined an "implementation" period where EU nationals could register to come and work in the UK.
The border between Northern Ireland and the Republic is one of the key issues that needs to be resolved by the UK and the EU before talks begin on a new trade deal.
British ministers had proposed using measures like surveillance cameras to allow free movement between the north and south of the island.
However, sources have told The Times that Mr Varadkar thinks these plans could jeopardise the peace process in Ireland and restrict movement between the two countries.
He is said to want customs and immigration checks moved away from the land border to ports and airports - effectively drawing a new border in the Irish Sea.
Irish foreign minister Simon Coveney, speaking at a meeting of EU foreign affairs ministers last week, said: "What we do not want to pretend is that we can solve the problems of the border on the island of Ireland through technical solutions like cameras and pre-registration and so on.
"That is not going to work."
He added: "Any barrier or border on the island of Ireland in my view risks undermining a very hard-won peace process and all of the parties in Northern Ireland, whether they are unionist or nationalist, recognise we want to keep the free movement of people and goods and services and livelihoods."
Such a suggestion is likely to anger the Democratic Unionist Party (DUP), which supports the Tories at Westminster through a confidence and supply arrangement.
The DUP has previously rejected calls for a "special status" for Northern Ireland after Brexit, while it is also at loggerheads with Sinn Fein after the collapse of the Northern Ireland executive.
DUP MP Ian Paisley tweeted: "1 of 2 things will now happen 1. A very hard border 2. Ireland will wise up and leave the EU."
On Thursday Ms Rudd commissioned the Migration Advisory Committee (MAC) to carry out a detailed analysis of the role of EU nationals in the UK economy and society.
In a letter to the MAC she outlined a transitional phase on immigration for EU nationals after Britain leaves the EU in March 2019.
She said there would be "a temporary implementation period to ensure there is no cliff-edge on the UK's departure for employers or individuals", including "a straightforward system for the registration and documentation of new arrivals".
After this period Britain would move to third phase of the policy, Ms Rudd said, which will determine the long-term arrangements around immigration from the EU.
In her letter Ms Rudd also said that after the UK leaves the EU, free movement will end, but migration between the UK and the EU will continue.
Immigration minister Brandon Lewis told BBC Two's Newsnight: "When we leave the European Union, by definition freedom of movement ends and we have control of our borders.
"There will be a system after March 2019, which will be our new immigration system, and there will be a period in that, as we've said, there will be transition system which includes a number of things."
Mr Lewis added that the Tories were "still very determined to deliver" their target of reducing net migration to the tens of thousands, but wanted to do so in a way that allows the economy to flourish.
Meanwhile, the Financial Times reported that Philip Hammond wants Britain to maintain full access to the European single market and customs union in the first of a two-part transitional deal after Brexit.
The Chancellor is said to have told business leaders he initially wants an "off-the-shelf" deal with the EU that would maintain the UK's current trading relationship with the bloc.
According to the newspaper, this would be followed by a second "implementation" phase while the final terms of a future trade deal were negotiated.
Allies of Mr Hammond told the newspaper the transition and implementation periods should end by 2022.
DUP MP Sir Jeffrey Donaldson ruled out the idea of a border running along the Irish Sea.
He told BBC Radio 4's Today programme: "There is no way that the DUP would go for an option that creates a border between one part of the United Kingdom and the other.
"Dublin really needs to understand that that proposition is absurd and unconstitutional."