Theresa May has made it clear the devolved administrations will not be given a decisive role in the UK's divorce from the European Union ahead of talks with leaders from across the UK.
The Prime Minister said she hoped the meeting would be constructive but warned they "will not agree on everything".
And she highlighted how the Supreme Court ruling on triggering Article 50 had set out "beyond doubt" that relations with Brussels would be determined by the UK government.
Mrs May said: "We will not agree on everything, but that doesn't mean we will shy away from the necessary conversations and I hope we will have further constructive discussions today.
"We have also had the Supreme Court judgment which made clear beyond doubt that relations with the EU are a matter for the UK Government and UK Parliament. We should not forget that that means MPs representing every community in the UK will be fully involved in the passage of Article 50 through Parliament."
Scotland's First Minister has warned Mrs May that she must take proposals from the devolved administrations seriously at a meeting of the Joint Ministerial Committee (JMC) in Cardiff on Monday.
Nicola Sturgeon wants Scotland to remain in the European single market even if the UK leaves, reflecting the majority Remain vote north of the border.
She said the UK Government was showing "no sign whatsoever" of taking Scotland's position "remotely seriously".
Proposals to remain in the single market have also been put forward by Welsh First Minister Carwyn Jones and Plaid Cymru leader Leanne Wood.
Calls for alternative settlements for the devolved administrations are on the agenda for the meeting.
It is also expected to focus on ways to help UK businesses to trade and invest in the run-up to Brexit.
Brexit Secretary David Davis, International Trade Secretary Liam Fox and the Secretaries of State for Scotland, Wales and Northern Ireland will also attend.
Mrs May said ministers from each nation had met three times since she had set out plans last October to "fully engage" with the devolved administrations during the planning for Britain's exit from the EU.
She added: "The United Kingdom voted to leave the EU, and the UK Government has a responsibility to deliver on that mandate and secure the right deal for the whole of the UK. We all have a part to play in providing certainty and leadership so that together we can make a success of the opportunities ahead."
Sinn Fein leader Michelle O'Neill, who is attending the talks, said the Conservatives were attempting to impose Brexit against the will of the people in Northern Ireland.
She said: "It is clear that Tory Government is seeking to impose Brexit against the will of the people in the north and of the people of Scotland. The Tory Government have effectively set aside the democratic process to pursue their own narrow political agenda. We need all of those opposed to Brexit to stand together.
"I will lay out the reasonable and achievable objective of the north being designated special status within the EU."
Mr Jones called for "open and frank discussions" about the UK's post-Brexit future.
He said he would be urging Mrs May to use the Welsh Government's EU White Paper as the starting point for forthcoming Brexit negotiations and would call on her to uphold promises made during the referendum campaign that Wales would not lose funding as a result of the UK leaving the EU.
The White Paper was published last week by Mr Jones and Ms Wood and sets out what they see as key areas including the importance of continued participation in the single market and "a balanced approach to immigration linking migration to jobs".
Mr Jones said: "I look forward to welcoming Government representatives from across the UK to Cardiff today.
"While we know that the UK will leave the EU we don't yet know how that will happen or what form our relationship with the EU will look like beyond that point."
Ms Sturgeon said: "It is becoming clearer with every day that passes that the UK Government is determined to pursue a hard Brexit and I am determined to do all I can to protect Scotland from the devastating impact that would have.
"In Scotland's Place In Europe we have set out a range of propositions to keep Scotland in the single market and these will be discussed at tomorrow's meetings. I hope the discussion on this tomorrow will be meaningful, but the process has been deeply disappointing so far."
She added: "Time is running out for the Prime Minister to demonstrate that she is going to uphold the commitment she made to me shortly after taking office that Scotland will be fully involved in discussions to develop an agreed UK approach and listen to alternative proposals for Scotland."
Mrs May will also hold talks in Dublin with Irish Taoiseach Enda Kenny.
Mr Kenny said: "This meeting will provide an opportunity for us to have a strategic and constructive discussion on issues of mutual concern and how we are going to work together to protect the interests of all our citizens on these islands."