The First Minister has said that she does not "generally use email to do government business", but the Times reported on Monday that Ms Sturgeon has been using a personal email address for official work since 2015 despite rules separating government and party.
Demanding that Ms Sturgeon publishes her emails from the SNP account she is alleged to have told government officials to use for urgent business, Tory MSP Donald Cameron said it would be "highly suspicious" if she failed to reveal the messages.
The Times reported that an SNP adviser instructed Scottish Government officials to send routine correspondence to her private secretary and direct urgent matters to her SNP account.
Questioned about the story on the BBC's Good Morning Scotland programme on Monday and asked whether the story was true, Ms Sturgeon replied: "Not really, no. I don't generally use email to do government business."
She said: "Routinely, the way you do government business is you get a box of papers and you put hand-written notes and then your private office turns them into emails.
"I don't want to get too complicated here. The story, as I understand it, in the Times is that my private office, out of hours if I don't have a private secretary with me and they need to get something to me urgently, will send an email.
"But that's coming from a Scottish Government email, it's in the system. It will be routine stuff like my diary for the next day. But the crucial point here is this - any government business, whatever platform it's done on, is subject to Freedom of Information."
Ms Sturgeon added: "The crucial point of Freedom of Information is that if I do government business, it doesn't matter if I'm doing it in a hand-written form or by email, if it's government business, it's subject to Freedom of Information and that is the basic principle of how that law works."
Mr Cameron, who raised the issue at First Minister's Questions last month, said: "The First Minister must come clean over her private email use and publish the emails from this account.
"It would appear that the First Minister and her team have not been entirely forthcoming and we have not been given the whole truth.
"I have written to the First Minister asking her to answer this simple question, does she use her private email account?
"The only way to clear this mess up is for her to publish the emails from this account.
"Anything less will be seen by Scots as highly suspicious - what does the First Minister have to hide?"
A spokesman for the First Minister said in response to the Times report: "This simply reinforces what we have said previously about the FM's personal email only being used to flag urgent, out-of-hours issues, which would normally relate to diary matters, such as travel arrangements.
"And any such emails sent from officials would be from government accounts, and subject to release under Freedom of Information (FOI).
"Unlike the UK Government, who have repeatedly refused to provide the emails and messages relating to the unlawful prorogation of parliament, the Scottish Government has been utterly transparent by releasing emails from personal accounts in response to FOI requests."