The UK government has confirmed it will seek to amend its Brexit bill without the consent of the Scottish and Welsh governments.
Cabinet Office Minister David Lidington said he remained confident that an agreement would ultimately be reached.
But he said the amendment would be published in time for it to be debated in the House of Lords.
He was speaking after the latest round of talks between the governments in London again ended without a deal.
The talks have centred on what happens to powers in devolved areas that return to the UK from Brussels after Brexit, with the devolved administrations accusing Westminster of planning a "power grab".
The Cabinet Office has said the amendment to the bill will mean that all EU powers that "intersect with devolved competencies" will go directly to Holyrood and Cardiff Bay.
But there would be a provision for the UK government to maintain a temporary "status quo" arrangement over a small number of returning policy areas where an agreement for a UK framework had not been reached in time for Brexit.
Mr Lidington said his Scottish and Welsh counterparts had used the latest meeting to make "constructive criticisms" of the proposed changes.
And he pledged to "consider further" suggestions they had put forward that would address their concerns that the proposals would still give Westminster a veto over some devolved areas.
And he said there was "no objection" from either the Scottish or Welsh governments to the amendment being published.
What is the row all about?
The dispute centres on 111 areas such as agriculture and the environment which are devolved but are currently run in part by the European Union.
The controversial Clause 11 of the Brexit bill proposes that these powers initially return to Westminster while UK ministers decide which frameworks should operate on a UK-wide basis.
The UK government has since proposed changes that would mean about 85 of these powers going straight to Holyrood, while the remainder will become part of UK-wide frameworks.
But the Scottish government says these proposals are still not acceptable as they would effectively give the UK government a veto over some of Holyrood's powers.
It has said it will withhold legislative consent for the EU Withdrawal Bill at Holyrood if an agreement is not reached, and has already introduced its own "continuity bill" at Holyrood.
Withholding consent for the Withdrawal Bill would not amount to a veto of Brexit, and would make things very difficult politically for the prime minister.
Mr Lidington said: "I am very pleased with the way in which things went, and I think we had a very constructive exchange of views and we all committed ourselves to continue the talks".
He added: "While I remain hopeful that a deal can still be done, we have a long-standing commitment to parliament to bring forward an amendment and will now table it - as discussed with the devolved administrations.
"I strongly believe our proposal would respect and strengthen the devolution settlements across the UK and do so in a way that still allows the UK government to protect the vitally important UK common market, providing much-needed certainty and no new barriers for families and businesses."
A letter obtained by the BBC ahead of the meeting suggested UK ministers want to publish details of which powers should apply UK-wide - which Mr Lidington also confirmed.
The Scottish government agrees the proposals should be published - but believes they will show the extent of the powers Westminster wants to take control of.
The letter also obtained by the BBC suggests that UK ministers have found it "difficult to counter" the "Westminster power grab" claims.
Key paragraphs from the letter
First Ministers Nicola Sturgeon and Carwyn Jones are due to hold talks with the prime minister next week.
But Scotland's Brexit secretary, Michael Russell, said the UK government amendment would still mean a "very substantial power grab" by Whitehall unless it was changed.
He said: "It was deeply disappointing that the UK government did not bring forward any new proposal today and are pressing ahead with a bill that, even with their proposed amendment, would allow them to unilaterally take control of devolved powers without the agreement of the Scottish Parliament."
Both the Scottish and Welsh governments have produced plans for continuity bills as a fallback option to deal with legal uncertainties caused by Brexit if they cannot agree to consent to the UK government's legislation.
Mr Russell said: "We have not agreed that amendment, that is absolutely explicit. They have not agreed the continuity bills.
"So we are proceeding on tracks that appear to be diverging, it is still possible for those tracks to come together and the aim of a meeting like today is to see if that can be done and we are trying to do so."
On Wednesday, the Scottish government's "continuity bill" passed its first vote at Holyrood by 94 votes to 30.
The bill would have the effect of bringing EU laws onto the domestic statute book ahead of Brexit.