The FBI search of Donald Trump's Florida home marked a sudden escalation of investigations into the former president
The FBI and Department of Homeland Security issued a memo to law enforcement around the country.
It said there had been an "increase in violent threats posted on social media against federal officials".
The FBI search last Monday was the first time a former president's home had been searched in a criminal probe.
Eleven sets of classified files were recovered from the property in Palm Beach, according to the warrant which was later made public. Mr Trump denies wrongdoing.
"The FBI and DHS would like to ensure that law enforcement, court, and government personnel are aware of the range of threats and criminal and violent incidents," the memo - which was seen by US media including the BBC's partner CBS - read.
It added that some of the threats were "specific in identifying proposed targets, tactics, or weaponry" and also made mention of the judge who authorised the search.
The memo, which was circulated late on Friday, also noted that a man wearing body armour had been shot dead by police after attempting to breach the FBI field office in Cincinnati, Ohio.
Hours before the incident last week, the suspect posted on Truth Social - Mr Trump's social media platform - of his intent to kill federal agents.
Jeffrey Ringel, a former FBI agent in New York, told the BBC that, while many threats prove to be "bravado", they can still have a major impact on staff.
"You're always looking over your shoulder," he says. "A threat in itself causes you to stop what you're doing because you're afraid of what might happen. You're thinking: 'What if?'"
"You go and work for the FBI because it has a great reputation and you want to do good," said Marion Bowman, a former assistant general counsel who has worked for the FBI. "For the people who are there now - this must be very dispiriting."
The search of Mr Trump's estate was part of an investigation into whether he improperly handled government records by taking them from the White House to Mar-a-Lago after he left office.
It triggered an angry backlash from his allies as well as Republicans in Congress, with some now calling for the affidavit - the sworn evidence that led to the search - to also be publicly unveiled.
"I think a releasing the affidavit would help, at least that would confirm that there was justification for this raid," Republican Senator Mike Rounds told NBC on Sunday.
"The justice department should show that this was not just a fishing expedition, that they had due cause to go in and to do this, that they did exhaust all other means," he said.
The justice department is not seeking to release the affidavit used to convince the judge that a search was necessary. Those documents would provide much more detailed information about how agents came to suspect that Mr Trump had committed criminal offences.
The search warrant, however, was signed off by a judge after prosecutors successfully argued that they had probable cause to believe a crime had been committed.
It was made pubic on Friday - a highly unusual move as warrants are normally not unsealed during a pending criminal investigation.
But Attorney General Merrick Garland - who leads the justice department - declared that there was "substantial public interest in this matter" and cited Mr Trump's public comments on the search as a reason for the warrant to be unsealed.
It revealed the three crimes Mr Trump is suspected of committing and what property had been seized.
Mr Trump has said he declassified the recovered documents before they were taken to Mar-a-Lago, although it is unclear whether this is relevant in a legal sense because the three criminal laws in question do not depend on whether the files were declassified.
The former president has not been charged with wrongdoing, and it remains unclear whether charges will be brought as a result of the investigation.
US attorney general: I personally approved Mar-a-Lago search warrant