Brexit Secretary Mr Davis attended a morning meeting of the joint ministerial committee (JMC) between the devolved nations, alongside Theresa May's right-hand-man Damian Green, for further talks around the current impasse on whether 111 powers should be returned to Scotland directly or via Westminster after separation from the bloc.
Ministers from around the United Kingdom have held talks on Brexit in London, the first such meeting for eight months.
Scottish Brexit minister Mike Russell has warned that should the bill pass through Westminster without consent from Edinburgh or Cardiff, there would be "trench warfare" over all subsequent pieces of Brexit legislation.
"We have been able to make some progress, including agreeing general principles that should ensure the role of the Scottish parliament in any potential UK- or GB-wide frameworks", said Michael Russell, Scotland's Brexit minister, in a statement.
However real differences remain, with the devolved administrations insisting the EU Withdrawal Bill be amended.
Mr Russell welcomed the agreement with Mr Green that there would be another JMC before Christmas, but criticised the UK's overall approach to talks with Brussels.
A Welsh government minister as well as a senior Northern Irish civil servant were also involved in the talks.
The formal group for discussing the exit negotiations was set up to allow Scotland, Wales and Northern Ireland to have their say on the Brexit process.
Scottish Secretary David Mundell said the agreement on the principles of how to move forward with powers returning to the United Kingdom from Brussels represented a "major step".
"On the day when the United Kingdom leaves the European Union, all parts of the United Kingdom need to be ready".
However, his claim that "talk of a power grab is now behind us" was immediately rejected by the Scottish and Welsh governments, who said they would still be unable to support the legislation unless it was substantially changed.
"I hope in our meeting on Monday we can agree on the principles for common frameworks that will deliver certainty and continuity to people living and doing business in the United Kingdom".
Despite the progress, the Scottish Government said it still intends to put forward amendments to the UK Government's Brexit Bill and can not recommend MSPs give their consent to the legislation.
The Scottish and Welsh governments have raised serious concerns over the EU (Withdrawal) Bill, which will see EU responsibilities in areas which would normally fall to devolved governments initially transferred to Westminster.