Even so, authorities are treating them as "live devices" not "hoax devices", New York City Police Commissioner James O'Neill said Thursday.
FBI officers investigating the serial mail bomber found two more suspicious packages on Friday, bringing the total to 12.
Robert De Niro is urging Americans to take political action after he (and a growing list of President Donald Trump's detractors) received a suspicious package thought to be a pipe bomb in an apparent nationwide plot to intimidate top Democrats who've publicly criticized the country's leadership.
Other packages have been intended for people including former President Barack Obama, Hillary Clinton, former Attorney General Eric Holder, philanthropist George Soros, former Vice President Joe Biden and Rep. Maxine Waters.
An X-ray of the package indicated a similar pipe bomb inside, and investigators suspect it was sent by the same person who sent explosives to Ms Clinton, Mr Obama and others, a law enforcement official said.
"Whoever is doing this is just trying to elicit a fear or disrupt something", said Ryan Morris, founder of Tripwire Operations Group, a company that provides explosives training to law enforcement and military officials.
Clapper said anyone who has criticized Trump should take extra precautions when handling their mail, adding: "This is not going to silence the administration's critics".
Trump long questioned Obama's US citizenship and referred to Clinton, whom he defeated in the 2016 presidential race, as "crooked Hillary".
The news came on a day when three more packages with potential bombs were discovered.
A police bomb squad and canine units joined federal investigators on Thursday to examine a sprawling United States mail distribution center at Opa-Locka, northwest of Miami, Miami-Dade County police said.
Two were recovered in California: one addressed to liberal donor Tom Steyer, who is leading a campaign to impeach Trump, and one addressed to California Sen. All the suspicious packages are believed to have gone through the USA postal system at some point, the source said.
The package addressed to him was discovered at a postal facility in Manhattan that is near several Broadway theaters.
The package addressed to Clapper was sent to CNN, which now hires him as an analyst.
A suspicious white powder found in an envelope along with the device sent to Brennan and CNN was tested and found not to be anthrax or other known agents, a source said. Sources told CNN the package was addressed to the senator's Camden, New Jersey, office. "They originated, some of them, from Florida", she said during an interview with Fox News Channel.
"Stop blaming others. Look at yourself in the mirror, your inflammatory rhetoric, your insults, lies and incitement to physical violence are shameful", has tweeted on Thursday, John Brennan, the former director of the Central Intelligence Agency, virulent detractor of the president, and specifically referred to by the package, filed Wednesday in the offices of CNN in NY.
"I thank God no one's been hurt, and I thank the fearless and resourceful security and law enforcement people for protecting us", De Niro said.
"It does remain possible that further packages have been or could be mailed", William Sweeney, assistant director of the Federal Bureau of Investigation, told an afternoon news conference in NY.
The officials weren't authorized to discuss an ongoing investigation and spoke Friday to The Associated Press on condition of anonymity. The president alluded to the shooting a year ago at a mostly Republican baseball practice outside Washington, D.C., in which Rep. Steve Scalise, R-La., was badly wounded. She is a former chairwoman of the Democratic National Committee. But Delaware authorities have said investigators have responded to post offices in Wilmington and New Castle. Two were intended for former vice-president Joe Biden at his home state of Delaware and one for actor Robert De Niro in Manhattan.
They were made of six inches of PVC pipe, a small block, a battery, wiring, and potentially explosive energetic material.
Like earlier targets, both Biden and De Niro have been sharply critical of Trump.
Three days after the first explosive device found in the home NY financier and donor to democrat George Soros, no one has yet been arrested.