On Thursday, without directly referencing the explosive devices, Mr Trump blamed the media for the "anger" in society.
At least one bomb was packed with shards of glass, one federal source said.
Notable among them is a 2002 arrest by Miami police for an offense described in online records as a "threat to bomb" and "threaten to discharge destructive device".
Speaking at the White House Friday afternoon, Trump congratulated law enforcement on the arrest and denounced what he called "terrorizing acts".
Another said "CNN Sucks", along with an image of Trump standing on a tank in front of fireworks and an American flag.
Mr Clapper said he is not surprised he has been targeted with a suspicious package.
Neither bomb got close to its intended target, and neither contained a written message, according to law enforcement officials. Bomb experts and security analysts say that based on their rudimentary construction it appeared they were more likely created to sow fear rather than to kill.
"Very unfortunate, what is going on", he said of the bomb drama and nationwide manhunt.
"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 told TheWrap.
In a statement released by his publicist, the actor said: "There's something more powerful than bombs, and that's your vote".
Those packages were removed late Thursday morning from DE postal facilities, law enforcement officials said.
DNA evidence reportedly links the unnamed mail to the suspicious packages.
Homeland Security Secretary Kirstjen Nielsen, in an interview Thursday with Fox News Channel, acknowledged that some of packages originated in Florida.
"I heard he was a person that preferred me over others", he told reporters.
Soros, the target of the first device, has always been a hate figure for right-wing groups and lives in Bedford, New York, not far from the Clintons.
Between Monday and Friday morning, packages containing supposed explosive devices were sent to George Soros, Hillary Clinton, Barack Obama, Eric Holder, Joe Biden, CNN's Manhattan office, Maxine Waters, Joe Biden, John Brennan, James Clapper, and Cory Booker.
Numerous packages had the return address of the Florida office of US Representative Debbie Wasserman Schultz, who formerly chaired the Democratic National Committee, according to the Federal Bureau of Investigation (FBI). Debbie Wasserman Schultz of Florida, the sources said.
One lead being pursued by investigators is that some of the devices may have been mailed from south Florida, but officials were cautious Thursday and urged the public to call in with tips from anywhere.
Three more devices were linked to the plot Thursday - two addressed to former Vice President Joe Biden and one to actor Robert De Niro - bringing the total to 10 in an outbreak of politically loaded menace with little if any precedent.
So far no one has been hurt. Nor would they say why the packages hadn't detonated, but they stressed they were still treating them as "live devices". It was found at a New York City postal facility and was similar to the other packages, the official added.
Wray declined to say if Sayoc is cooperating with investigators. Bomb experts and security analysts say based on their rudimentary construction it appeared they were probably created to sow fear than kill. Each had computer-printed address labels and six stamps, the agency said. "We must never allow political violence to take root in America and I'm committed to doing everything in my power as president to stop it and stop it now". His supporters accused Democrats of unfairly suggesting the president was to blame for the bomb scare.
Its marking and contents appear similar to the other pipe bomb packages, two law enforcement sources said.