The New York City police commissioner, James P. O'Neill, said at a news conference that the packages contained live devices that should be treated with the utmost seriousness.
A bomb squad unit removed a package that was addressed to the Hollywood actor at his office in Manhattan.
The FBI, US Secret Service and police were conducting a nationwide manhunt for the culprit or network of people behind at least 10 suspect packages that politicians on both sides of the aisle have branded terrorism.
Earlier, the Federal Bureau of Investigation said a suspicious package addressed to New Jersey Democratic Sen.
The episode sparked an outcry from Trump's critics, who charged that his inflammatory rhetoric against Democrats and the press was creating a climate for politically motivated violence.
The list of bombing targets spread from New York, Delaware and Washington DC to Florida and California.
These packages - recovered in Florida and NY - push the total number of devices found by law enforcement authorities to 12.
A package was intercepted at a NY post centre, reportedly addressed to James Clapper.
The first crude bomb to be discovered was delivered on Monday to the suburban NY compound of George Soros, a liberal billionaire and major contributor to Democratic causes.
Trump, in a tweet Thursday, blamed the "Mainstream Media" for the anger in society.
The discoveries - making 12 so far - further spurred a coast-to-coast investigation, as officials scrambled to locate a culprit and possible motive amid questions about whether new packages were being sent or simply surfacing after a period in mail system.
United States law enforcement is engaged in a frantic search for the person or persons who sent explosive devices in the mail to De Niro and other people.
The complaint also included details suggesting Sayoc's antipathy toward the people and organizations targeted, including CNN, where one packaged was found and another addressed.
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On Friday, shortly before news of the arrest broke, he complained that the packages were slowing momentum for his Republican Party ahead of the November 6 elections, remarks that enraged his opponents.
Authorities pleaded with the public to send in any tips, and William F. Sweeney Jr., assistant director in charge of the FBI New York field office, said people should remain vigilant, warning that more devices "have been or could be mailed".
De Niro has been a frequent critic of Trump and used an expletive to condemn the president at the televised Tony Awards last June, receiving a standing ovation.
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.
Trump declared that "these terrorizing acts are despicable" and said Americans "must unify". Debbie Wasserman Schultz's office is housed in Sunrise, Florida, Oct. 24, 2018.
Bomb experts and security analysts say that based on the rudimentary construction of the bombs it appeared they were more likely created to sow fear rather than to kill.
New York's Democratic mayor Bill de Blasio urged people across the city to be on alert, and to refrain from opening suspicious packages.
After initially condemning the attempted bombings, while delivering prepared remarks at the White House calling for unity, Trump then blamed the media for the state of affairs - after an explosive device was delivered to CNN's office in NY.
A picture from CNN of the package sent to Robert De Niro.
"There's no blame. There's no anything", Trump said.
"It's become so bad tempered and spiteful that it is beyond all description", he added.
"No nation can succeed that tolerates violence", Trump told the audience.
"Let's get along", he said at a Wisconsin rally on Wednesday night.
You can also see another shot of what appears to be the suspect's van below.