CNN did not learn how specific the threats were, but law enforcement agencies treated them seriously and out of an abundance of caution, the US Marshals Service and local police increased patrols and protective officers to provide security for some of the judges, the officials said.
A spokesperson from the US Marshals Service declined to comment directly on the threats but said that while "we do not discuss our specific security measures, we continuously review the security measures in place for all federal judges and take appropriate steps to provide additional protection when it is warranted."
The threats come as Trump continues his verbal criticisms of judges -- something that has drawn concern from former law enforcement officials and others who fear that public officials should not target a specific judge, and instead base their criticism more broadly on a court's ruling.
Security experts say that while Trump's comments were clearly not meant to put the judges' safety at risk, in general, public officials should avoid comments against a specific judge so as not to spur an unhappy litigant.
"Federal judges are constantly under some kind of threat around the country, and the US Marshals investigate hundreds of threats every year on the federal judiciary," said Arthur D. Roderick, who is a retired assistant director for investigations for the US Marshals.
"Anybody that has looked at what the US Marshals do has got to realize that an attack on any judge is an attack on the rule of law of the United States," he said, noting that the President's sister is a federal judge and the President should be familiar with threats against judges.
But Leonard Leo, an adviser to Trump on the Supreme Court, says it is a "huge stretch" to equate the criticisms that President Trump has made with a threat to judicial security.
"President Trump is not threatening a judge, and he's not encouraging any form of lawlessness," Leo said. "What he is doing is criticizing a judge for what he believes to be a failure to follow the law properly."
"Judges are given life tenure so they can go wherever the law takes them knowing that they can resist being unduly influenced by criticism or by praise," Leo said, adding that "all the way back to Thomas Jefferson, there has been criticisms by Presidents as well as (the) general public."
On Thursday, White House press secretary Sean Spicer was asked whether Trump regrets his criticism.
"He has no regrets," Spicer said.
Trump's criticism were based first on Judge James L. Robart, who halted the executive order pending appeal. Trump referred to him as a "so-called" judge.
Later he suggested that Robart's ruling could put the country in peril.
"Just cannot believe a judge would put our country in such peril. If something happens blame him and court system. People pouring in. Bad!"
In a speech Wednesday to the National Association of Sheriffs, Trump reiterated that his executive order is meant to protect "the security of the country."
But he took the unusual tack of criticizing the judges currently hearing the appeal.
"I don't ever want to call a court biased and we haven't had a decision yet. But courts seem to be so political, and it would be so great for our justice system if they would be able to read a statement and do what's right," Trump said.
He said, "I will not comment on the statements made by certainly one judge, but I have to be honest that if these judges wanted to, in my opinion, help the court in terms of respect for the court, they'd do what they should be doing. It's so sad."
A federal appeals court ruled Thursday
Trump's travel ban will remain blocked. The unanimous ruling from a three-judge panel means that citizens of seven majority-Muslim countries will continue to be able to travel to the US, despite Trump's executive order last month.