The First Minister, who headed to London on Wednesday morning ahead of the no confidence vote in Theresa May’s Government, said it was “not obvious” that the PM “has any real idea what to do next”.
The SNP leader spoke after the Prime Minister suffered a historic defeat in the House of Commons, with MPs rejecting the withdrawal agreement she has negotiated by a majority of 230.
While the Tory leader is expected to survive the vote of no confidence, what will happen next with regards to exiting the European Union is less clear.
Ms Sturgeon’s SNP, as well as the Liberal Democrats, are calling for the issue to be put to the people again in a second referendum, but Labour favours a general election.
The First Minister spoke to Mrs May following Tuesday night’s historic defeat in the Commons - which was the biggest government defeat on a meaningful vote for at least a century.
She tweeted that while she had had talks with the Conservative leader, it was “not obvious that she has any real idea what to do next”.
Ms Sturgeon added: “Also not at all clear she is open to any fundamental change of thinking in her proposed cross party talks.
“The bare minimum she must do now is seek extension of Article 50 to stop the clock.”
As she headed to London to meet SNP MPs, including Westminster leader Ian Blackford, she stated: “We want UK to stay in EU which is why we back a #PeoplesVote.
“But it is becoming increasingly clear that Scotland’s wider interests will only be protected with independence.”
Tory MPs however accused the First Minister of using the Brexit vote to push for a second independence referendum.
Stephen Kerr, the Conservative MP for Stirling, told BBC Radio Scotland’s Good Morning Scotland: “The SNP has been clear again this morning by Nicola Sturgeon’s tweet, they are only interested in this subject for one reason and that is to bring about the second independence referendum.
“Nicola Sturgeon was up at the crack of dawn on her way to London and she took time to tweet about a second independence referendum.”
Mr Kerr, who voted for the withdrawal agreement, added: “Whenever it looks like the SNP might be in a position where they are prepared to talk in substance about how we bring about an orderly Brexit, they change their position, because they are not interested in an orderly Brexit, what they are interested in is a chaotic Brexit.”
Fellow Tory Douglas Ross, who voted against the Brexit deal, hit out: “The SNP don’t want a good deal or a deal at all.”
He claimed Scottish nationalists “want to disrupt Brexit as much as possible and use it as a tool to enhance their chances of holding and winning a second independence referendum”.
Mr Ross also told BBC Radio Scotland that the massive scale of the PM’s defeat could encourage the other European nations to look again at the deal and make changes to it.
He said: “The comprehensive defeat of this deal, mainly around the backstop issue, will focus minds both in the United Kingdom but more importantly in the European Union because they also want a deal, they don’t want a no-deal Brexit.”