Scottish politicians passed a motion on Tuesday stating it does not consent to the UK Government's EU Withdrawal Bill, which Brexit-supporter Bernard Jenkin said revolved around a "manufactured row".
But it has also named 24 areas where it wants to retain power temporarily in the wake of Britain's exit from the European Union, including in areas such as agriculture, fisheries and food labelling.
The Labour-run Welsh Government previously shared the position of Scottish ministers, but dropped its opposition following changes to the legislation. "It's about a technical process of agreeing things that we've already agreed, and that's why I find it nearly incomprehensible that we've got into this debate around what's really a very, very technical issue".
Scottish Green co-convener Patrick Harvie was also clear his party's MSPs would "not consent to the UK Government's assault on the powers of the Scottish Parliament".
If no deal between Edinburgh and London can be reached, Westminster has the option of introducing the Withdrawal Bill against the wishes of the Scottish Parliament. "But this is about protecting devolution which the people of Scotland voted for overwhelmingly, and there is no mandate to undermine that".
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The exchange in the Commons came after Scottish Secretary David Mundell claimed that some MSPs appear to have a "fundamental misunderstanding" of the Brexit legislation.
Speaking after the vote, he said any move to force legislation on Holyrood would break a "20 year old devolution settlement".
Meanwhile, Scottish Liberal Democrat Europe spokesman Tavish Scott said: "The Brexit process has been chaotic and the treatment of the devolved administrations has been shoddy".
Peter Ross, Stranraer Liaison Group chairman, added: "We are delighted to be welcoming the Scottish Rural Parliament to Stranraer".
Nicola Sturgeon's government in Edinburgh insists that Holyrood must explicity agree to any changes before they can take effect.
If May chooses to disregard the Scottish vote, it could fuel First Minister Nicola Sturgeon's calls for a second referendum on Scottish independence and likely strengthen her argument that Scotland should be independent.