Alex Salmond said the Department for Work and Pensions (DWP) should withdraw the memo telling staff they should support the UK Government's objective to keep Scotland in the UK, claiming it showed the "Westminster government apparently dictating to its employees".
But pro-union campaigners accused the SNP leader of "turning hypocrisy into an art form" after his Health Secretary Alex Neil wrote to NHS workers in a bid to reassure them about pension arrangements after a Yes vote.
Mr Neil told health workers: "Independence will deliver a public-service pensions system that is affordable, sustainable and fair, one that works for and with public-sector employees, public-service provision, the taxpayer, and the overall public finances.
"Independence will enable a positive and inclusive approach to negotiating public-sector workers' pension arrangements."
The letter to DWP staff reportedly said: "It is important that, as civil servants, we understand why the Scottish independence referendum is different from elections such as a UK general election or a European election.
"This is because the UK Government has a clear position to maintain the union and so it is legitimate and necessary for UK civil servants to support the Government in this objective."
Dave Penman, general secretary of senior civil servants' union the FDA, said the memo was "ill-judged" and added: "It is factually accurate but it probably could have been written a lot more sensitively."
A DWP spokesman insisted: "Of course the department has not told its staff, or anyone else, how to vote.
"It was an open letter to all DWP staff setting out Scottish referendum guidance and the role of the civil service. Similar advice has been issued by the Scottish Government."
Mr Salmond branded the DWP memo as "quite extraordinary" and said: "The unions were furious, and rightly so, because it is no part of what a government should be doing, the Westminster Government apparently dictating to its employees.
"Now maybe it's just badly worded, maybe that's not what they meant to say. Well, if that is the case, they should withdraw the letter and apologise to their staff.
"It's not something the Scottish Government would ever do, give the impression that we've got the right to dictate to our employees. You don't have the right."
Labour MSP Jackie Baillie said the First Minister's remarks were "the height of hypocrisy from the nationalists".
She added: "On the day that they are complaining about the UK Government contacting staff, the SNP Scottish Government are doing the exact same thing behind closed doors.
"This is typical of the nationalists - they say one thing in public and an entirely different thing in private. It's no wonder Scots don't trust a word they say."
Scottish Liberal Democrat health spokesman Jim Hume said: "As senior nationalists took to the airwaves to express mock outrage over UK Government guidance to civil servants over referendum purdah rules, the Health Secretary was contacting NHS Scotland staff extolling the virtues of his independence plans.
"This is further evidence that nationalists will say anything to anyone to try and increase support for independence. They have turned hypocrisy into an art form."