Scotland said on Thursday progress was being made towards a deal to ensure that all devolved powers transfer back to Scotland, Wales and Northern Ireland after Brexit.
The Scottish and Welsh governments have accused the Westminster-based British government of staging a power grab with its European Union (Withdrawal) Bill, which will largely "copy and paste" EU legislation into British law.
They have sought assurances that the powers currently devolved to them in areas such as fishing, farming and the environment will return to them rather than to London when Britain leaves the EU in March 2019.
"We have worked closely with the devolved administrations to find a way forward that respects the role of the devolved governments and ensures we are able to protect our vital UK internal market," David Lidington, Britain's cabinet office minister, said in a statement.
"The proposal that we have put on the table is a considerable offer that I hope the devolved administrations will engage with constructively."
The government said the changes it had made would mean that the vast majority of powers would automatically flow from the EU to the devolved administrations. However the Scottish and Welsh governments are seeking legal protection for their current powers.
"Progress is being made and we will continue to talk. I will continue to fight for the best deal for Scotland," said Scotland's Brexit minister Michael Russell after the meeting.
The British parliament must seek consent from the Scottish and Welsh assemblies when legislating on policy areas that overlap with their devolved powers. But both have declined to give their consent to the withdrawal bill because they say it fails to respect the devolution agreement made 20 years ago.
While they do not have a veto on Brexit legislation, ignoring them would stretch already tense relations with London, and could feed public appetite for Scottish independence.
Russell said the British government needed to take more steps to safeguard devolution and that Scotland would continue to argue for Britain to remain part of the EU's single market and customs union. That possibility is something Prime Minister Theresa May's government in London has ruled out.
"We are not opposed to UK-wide frameworks, when they are in Scotland's interest, but devolved powers can only be changed with the agreement of the Scottish parliament," said Russell.
"Failing that commitment from the UK government, we will be unable to recommend consent to this legislation."