The threat, if carried out, would mean a black mark going on an officer's appraisal.
Brian Docherty, chair of the Scottish Police Federation, said police chiefs "can't put out that sort of email".
Police Scotland's policy of stop and search, which is aimed at detecting drugs, knives and other illegal items, has become embroiled in a number of controversies.
After it was revealed that young children and babies were searched on a "consensual" basis, the force scrapped the practice.
The police inspectorate is also investigating allegations that officers have been claiming bogus searches to inflate the figures.
Several police sources have also told this newspaper officers feel under pressure to meet divisional expectations on stop and searches.
A recent report by the Scottish Police Authority, which oversees the force, concluded: "Some officers indicated that they felt pressure to conduct a certain number of searches. This view was confirmed by the same representatives of police staff associations."
An internal email to police managers at Dunfermline police station appears to confirm these fears.
An increase in anti-social behaviour in a Dunfermline ward triggered an instruction that stop and search in this area needed "pushed".
The email noted: "I fully expect staff carrying out their duty in this respect and need to see a substantial return over the next few weeks."
However, there was also a warning: "I also expect those not recording stop searches to be firmly dealt with by way of PDR."
PDR, which stands for performance development review, is the appraisal system by which officers are monitored and assessed.
Police Scotland has always denied setting targets for individual officers on stop and search, but a force insider said of the email: "Management are using threats to ensure that stop-and-search numbers increase. As you can imagine, this is having a huge effect on the morale of an already broken workforce.
"Fearing a negative PDR, officers are submitting stop and searches that are made up or undertaken with no justification. This obviously has a knock-on effect in the community."
In the Fife area, there were 7414 searches between April and December 2013, up from 1442 during the same period in 2012 - a massive 414% rise.
Fife, the area with by far the biggest rise, has been chosen for a pilot of a reformed version of stop and search.
Under the scheme, parents of children searched will be given a letter explaining the reasons for the action.
Docherty said: "We've raised similar concerns over the last year with Police Scotland. If you are putting out one message in public, and managers are saying something else in private, the result is a skewed message.
"Anybody overstepping the mark needs to be asked to explain why they are doing this. You can't put out that sort of email."
Alison McIness, Scottish Liberal Democrat justice spokeswoman, said: "This confirms our suspicion of the existence of a targets culture in Police Scotland. This threat from a superior to negatively mark officers' records over stop-and-search targets must be investigated thoroughly. Anything less risks seriously damaging relationships within the ranks.
"Placing value on increasing the total number of stop and searches needed will do nothing to drive down the significant margin between searches and positive results."
A Police Scotland spokesperson said: "After an increase in anti-social behaviour in a Dunfermline ward the local management team identified a number of interventions to be taken which included additional high-visibility patrols, community team revisits and the use, where appropriate, of stop search.
"The comments selected were from a more detailed internal email from a manager to other managers which highlighted the fact that this was an issue in this particular ward and that officers should be using all means at their disposal, including stop and search, to ensure that this increase in anti-social behaviour was dealt with appropriately."