Scottish Brexit Minister Mike Russell will now write to Theresa May's de facto deputy, David Lidington, calling on him come to Scotland and hear "hear the concerns of all parties and to discuss with the Scottish Government and the UK Government any new ideas from any of the parties".
Scotland voted against independence by 55 percent in a referendum in 2014, but Sturgeon insists she has a mandate to hold a second vote since Scotland voted against Brexit by 62 percent in 2016.
However, Scottish Government Brexit minister Michael Russell has put forward a motion stating that Holyrood will refuse permission for the changes on the grounds it would "constrain the legislative and executive competence of the Scottish Parliament and Scottish Government".
Scottish politicians at Holyrood refused to give their backing to a key piece of Theresa May's Brexit legislation, paving the way for a constitutional crisis. It also risks playing into the hands of the nationalists who are trying to build a case for another independence referendum. "But the government might ultimately feel it has no alternative". The SNP had its wings clipped and the narrative shifted to how Scotland can keep the powers it has after Britain leaves the EU.
"I feel if we could put all the constitutional hoo-ha, all the bickering and politicking aside, both Scotland's governments could work together to get us a really good deal from leaving the European Union", he told BBC Radio Scotland.More news: Government Officials Drive The George Soros Foundation Out Of Hungary
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The Scottish vote came as Ms May's cabinet subcommittee on Brexit met amid enduring differences over Britain's customs relationship with the European Union after Brexit.
Scotland is responsible for its own education, health and transport policies as well as the judicial system and some financial affairs.
The British government said it would refer that bill to legal officers and a hearing is scheduled for July in the Supreme Court unless agreement can be found before then.
Mr Mundell said Brexit would leave the Scottish Parliament with more powers and responsibilities than it now has, and pointed out it had recently been handed powers over income tax the welfare system.
United Kingdom ministers are likely to continue their negotiations with their Scottish counterparts and hope to come up with a deal and put the vote to MSPs again.