They have supported first minister Nicola Sturgeon's call for a second referendum on Scottish independence.
Just two days before the British leader launches the formal divorce procedure with the EU, May wants to try to stem demands in Scotland for a new independence referendum which could rip apart the world's fifth largest economy and encourage nationalists in Northern Ireland to follow suit.
But Sturgeon has argued that last year's British referendum on the European Union - in which a majority of Scottish voters chose to remain in the bloc and a majority of English voters opted to leave - represents a "material change in circumstances" and that Scotland risks being taken out of the European Union against its will.
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Her motion asked MSPs to back her in approaching the British government to seek permission for the referendum.
Scotland's First Minister, Nicola Sturgeon (R), greets Britain's new Prime Minister, Theresa May, as she arrives at Bute House in Edinburgh, Scotland, Britain July 15, 2016.
The minority Scottish Government won the vote thanks to support from the Scottish Greens, and following an extended debate which was delayed by a week due to the Westminster terror attack.
"Scotland has a longstanding relationship with the United States which spans family, friendship and business and this government is committed to continuing to strengthen these ties", she said.
May also took the opportunity to reiterate her opposition to Sturgeon's call for another independence referendum.
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The council will meet again on March 31, and will likely approve the items in each tax category. The minister on Friday passed the motion on government business for the coming week.
Then there is the question of the official procedure for setting the question and deciding other matters; there also needs to be a decent time for a proper campaign - a referendum can not be held the day after the end of the Brexit talks.
May's London-based government would have to approve a legally binding referendum, and May says "now is not the time" for a new independence vote.
"What she did do though and did very clearly, and I pressed her very hard on this, was to confirm she wanted the terms of Brexit, including the terms of the UK's future relationship with the European Union to be clear in around 18 months to two years time".
Scotland Secretary David Mundell said: "We're not entering into negotiations on whether there should be another independence referendum during the Brexit process".
Neither leader has expressed a willingness to compromise and the rift is unlikely to end before Article 50 is triggered.
He said, "All of us want the best for Britain".
At one stage, Scottish Conservative leader Ruth Davidson told Sturgeon to "sit down" during a heated exchange with the Scottish First Minister.
"It's not appropriate to have a referendum whilst people do not know what the future relationship between the United Kingdom and the European Union is and they won't know that until the Brexit process is complete".