Theresa May has offered to involve Scotland, Wales and Northern Ireland in regular formal talks on the Brexit process in an effort to quell concern about her handling of the situation.
Downing Street said Mrs May will tell the leaders of the devolved administrations concerned about a possible hard Brexit that final decisions about her approach had not yet been taken and "how the UK leaves the EU will not boil down to a binary choice".
Mrs May will come under pressure from Scottish First Minister Nicola Sturgeon, Welsh counterpart Carwyn Jones and Northern Ireland's leader Arlene Foster and her deputy Martin McGuinness at a meeting in Downing Street.
The devolved administrations are keen to secure continued participation in the single market and want to hold votes on Mrs May's approach before she triggers Article 50, formally beginning the Brexit process.
The Prime Minister has offered them a "direct line" to Brexit Secretary David Davis, who will chair a new forum bringing together representatives from Westminster, Holyrood, Cardiff Bay and Stormont for regular talks on the situation.
Mrs May is hosting the first meeting of the Joint Ministerial Council (JMC) since 2014 on Monday.
Ahead of the talks, officials insisted she was "ready to listen to proposals" put forward by the first ministers about the Brexit process.
Mrs May said: "I am determined that as we make a success of our exit from the European Union, we in turn further strengthen our own enduring union.
"The great union between us has been the cornerstone of our prosperity in the past - and it is absolutely vital to our success in the future.
"The country is facing a negotiation of tremendous importance and it is imperative that the devolved administrations play their part in making it work.
"The new forum I am offering will be the chance for them all to put forward their proposals on how to seize the opportunities presented by Brexit and deliver the democratic decision expressed by the people of the UK."
If the devolved governments agree, a new sub-committee of the JMC chaired by Mr Davis would hold its first meeting by the end of November and at least one more by Christmas as negotiations progress before Article 50 is triggered by the end of March 2017.
But leaders in Wales and Scotland have called for the UK Parliament and the three devolved legislatures to be given their own votes on the negotiating position the Government intends to take and said that Article 50 should not be triggered until there is an agreed approach.
"We believe that a UK Negotiating Framework should be developed, based on principles and aims (but without revealing a detailed 'negotiating hand') and this, linked to invoking Article 50, should be the subject of a vote in all four of the United Kingdom's parliaments and assemblies," Mr Jones said in a letter to the Prime Minister.
"Such an approach would properly reflect the stated position of the UK Government that the UK is a family of nations, a partnership of equals."
He also said the final "exit deal" should also be subject to votes in all four UK parliaments and assemblies.
Ms Sturgeon backed Mr Jones' position, telling the Prime Minister: "It will not be acceptable for the devolved administrations to simply be consulted on UK Government plans. We must have meaningful input into the decision making structure and the formation of negotiating positions."
In a hint at the prospect of a second independence referendum, she added that "all possible options" were being considered.
She told Mrs May: "As you know following Scotland's unequivocal vote to remain in the EU, the Scottish Government has a democratic duty to protect all of Scotland's interests and we are considering all possible options to ensure Scotland's continuing relationship with, and place in, Europe.
"I welcomed your willingness in July to consider proposals for different arrangements for Scotland as part of this process and will set out those proposals in the coming weeks.
"I believe there is an obligation on all of us to try to work out solutions that will allow the vote in each of our administrations to be respected."