An investigation is under way into the leaking of a letter warning against leaks, Downing Street has said.
The memo from Cabinet Secretary Sir Jeremy Heywood warned officials that Theresa May had demanded urgent action to tighten security in Whitehall.
The letter's existence emerged after it was leaked to The Mail on Sunday.
Unions have defended civil servants, who face losing their jobs if they leak material even if it does not put national security at risk.
General secretary of the FDA union, Dave Penman, said: "Ask any journalist worth their salt and they'll tell you that the vast majority of leaks emanate from politicians.
"Civil servants are being threatened with the loss of their livelihood if they are caught leaking. A similar sanction should apply to politicians, not simply the loss of the trappings of ministerial office."
The letter leaked to the Mail on Sunday said "security teams" would take charge of beefed-up leak inquiries with the power to demand access to phone and email records.
The paper said it also said ministers and officials must use officially supplied Whitehall mobile phones to stop them using private mobiles and emails to leak secrets.
Asked about the latest leak, Mrs May's official spokeswoman said they would follow the "usual process", adding: "Action is being taken to follow up and investigate that."
"There will be investigations and appropriate action taken if perpetrators are identified."
The spokeswoman said that unauthorised disclosures were taken "extremely seriously" and that the civil service code made clear how officials should behave with regard to classified information.