After admitting last Thursday's result, in which the SNP lost 480,000 votes Scotland-wide, raised substantial questions about her quest for a second independence referendum, Sturgeon is anxious to reassert herself and underline her party's relevance.
The independence referendum of 2014 was won by "No" to independence, by 55% to 45% who voted "Yes".
The UK Government is seemingly divided over how to approach negotiations to leave the European Union with talks due to start next week.
Sturgeon is one of several politicians who want to change May's mind over Brexit after the ruling Conservative Party lost its parliamentary majority in a national election last week.
The SNP remained the largest party in Scotland with 35 seats, but lost 21 of its 56 constituencies compared with 2015.
Nicola Sturgeon has today warned the Prime Minister that the Scottish Government and other United Kingdom devolved administrations could derail the final Brexit deal as she stepped up calls to be involved in negotiations.
She said all Scotland's political leaders had endorsed her call for a softer Brexit, which puts heavy emphasis on access to the single market.
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Independence agitator in chief Alex Salmond, and the SNP's Westminster leader Angus Robertson were two of the high profile scalps to be claimed on election night.
Nicola Sturgeon has called for Theresa May to pause the Brexit negotiations to build a new cross-party, "four-nation" consensus on the UK's stance with the EU.
She said people are "becoming increasingly anxious about the confusion surrounding the UK's position", with Theresa May yet to appoint a negotiating team with a "stable mandate".
"The election result was a comprehensive rejection of the Tory plans for an extreme Brexit - and single market membership must now be back on the table", he said.
Scottish Tory leader Ruth Davidson, pictured outside Stilling castle on Saturday.
He added: "This poll makes it abundantly clear that Nicola Sturgeon must immediately drop her plans for a divisive second independence referendum".
"I have said that I will reflect on the election result in Scotland, listen to voters and consider carefully the best way forward for Scotland", she wrote in her letter. "The strongest possible position in the Brexit negotiations will be one that is backed by all parties and all governments across the United Kingdom".
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