The SNP leader has already written to the Prime Minister and the five Tory MPs seeking to replace him, calling for such a guarantee.
But with none being made, she stepped up her efforts after meeting with European consuls in Edinburgh.
Ms Sturgeon said many of the consuls had “reported concerns and anxiety on the part of their nationals living here in Scotland”.
She said: “That is understandable, because there has been a huge question mark placed over their right to live here – not immediately but in the future – as a result of the EU referendum.”
Since the Brexit vote, Ms Sturgeon and her team of ministers have stressed they welcome the contribution residents from other parts of the EU make.
The First Minister said: “There was a welcome for the message the Scottish Government has given, that we consider EU nationals to be welcome here, that we value their contribution and consider Scotland to be their home. That is a message I am very keen we continue to get across.”
But she added: “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.
“There is no doubt that any uncertainty that is being felt could be ended if the UK Government simply gave a guarantee that no matter what happens in the negotiations, people who are already living here, have already built lives here, will have the right to stay. That could be done quickly, simply and straightforwardly and I think it is disgraceful that it hasn’t been done.”
Scottish and British people living and working in other parts of Europe “have similar anxieties”, Ms Sturgeon said, and she added: “I would hope similar guarantees would be forthcoming from other European countries to them.”
She stressed: “Clearly we would be in a stronger position in arguing for that if the UK was giving guarantees to nationals living here.
“People in both directions that have chosen to live in other countries across the European Union are making contributions, they’ve built their lives, they shouldn’t be used as some kind of negotiating chip, and that is the inhumane aspect to all of this.”
The First Minister was also holding talks with Scotland’s leading business organisations to hear their concerns about the impact of Brexit.
“Clearly there is a period of significant uncertainty and the risk of a significant impact on the economy ahead of us,” Ms Sturgeon said.
She again highlighted her “determination to find a way of protecting Scotland’s place in the European Union”, but also said: “I’m very keen to work with the business community to get a message out there across Scotland, the UK and Europe as a whole that Scotland remains open for business and we are a good place to do business.”