And she stepped up calls for David Cameron and those bidding to succeed him to make a clear commitment on the issue.
Her comments came as Home Secretary Theresa May was confirmed as frontrunner in the race to become the next Tory leader and Prime Minister.
In the first round of voting by Conservative MPs, Mrs May got 165 votes – one more than all the others put together. Energy Minister Andrea Leadsom was next with 66. Justice Secretary Michael Gove got 48 – better than some expected after his “knifing” of Boris Johnson.
Work and Pensions secretary Stephen Crabb got 34 votes, and announced he was withdrawing from the race and backing Mrs May.
Former Defence Secretary Liam Fox finished bottom of the poll with 16 votes and was eliminated. He has given his support to Mrs May. The choice between the final two candidates will be down to party members. Mrs May has refused to guarantee the rights of EU nationals living in the UK because she believes it will be a factor in the Brexit negotiations. But Ms Sturgeon insisted people from other countries who had come to the UK and made their lives here should not be used as a bargaining chip in a wider discussion with Europe.
The First Minister yesterday met European consuls in Edinburgh and said many of them had “reported concerns and anxiety on the part of their nationals living here in Scotland”.
She said: “This uncertainty the EU nationals are living with could be ended at a stroke if the UK government and all of the candidates for Prime Minister simply said that their right to live here was guaranteed regardless of what happens in the EU negotiations.
“It’s regrettable that hasn’t happened on the part of everybody and I call again on the UK government to give that categoric guarantee to people who have built their lives here, who’ve got jobs here, pay taxes here, raised families here.
“They shouldn’t be used as a negotiating chip in a wider discussion with Europe.”
Bank of England governor Mark Carney yesterday announced steps to ensure British banks could keep lending in the aftermath of Brexit. He said the Bank would lower the amount of capital banks are required to hold in reserve, freeing up an extra £150 billion for lending.
The move came as the pound plunged to a new 31-year low.
Mr Carney stopped short of repeating concern about a possible recession, but said there was the “prospect of a material slowing of the economy” following the referendum result.