The Government is being urged to seek a special meeting of EU leaders to finally resolve the backstop issue for the Irish border.
Labour Party Leader, Brendan Howlin says the position paper agreed by the UK on Friday is a step forward, but the practicalities of permanently avoiding a hard border are still unclear.
He says we need to resolve the border question well in advance of the October EU Council deadline.
"The incoming president of the European Council has called a special EU Council for September 20 but I think it is now incumbent on the Irish government to ensure that there is a second item attached to that agenda and that is the legal interpretation of the backstop arrangements so that when we come into October we can do it with clear knowledge that the Irish border situation has been resolved," said Mr Howlin.
Meanwhile, farmers' representatives say Britain's Brexit proposals show an unacceptable amount of 'double-think'.
Irish Farmers' Association (IFA) President Joe Healy says that while the statement shows some sign of movement - it also shows a generous helping of "wanting to have their cake and eat it".
"The statement falls short of the commitment and clarity required by farmers," said Mr Healy.
"For example, the proposed facilitated customs arrangement and EU-UK Free Trade Area where the UK will control its own tariffs and trade with the rest of the world will not work for agriculture and food.
"We feel that it would allow the UK to open the floodgates to cheap food imports and allow them to pursue a cheap food policy that would destroy the UK market for Irish farmers."