Sayoc was formally charged with sending 13 such devices, and a law enforcement official said he is likely to be charged with sending a 14th device to Mr Tom Steyer, a major Democratic donor.
Clapper said on CNN Friday morning he was not surprised he was targeted and said the incidents were "serious".
Authorities have not said whether the van seized in Florida was linked to Sayoc.
Court records show he had been arrested at least nine times, mostly in Florida, for accusations of grand theft, battery, fraud, drug possession and probation violations.
The front page of the print edition of the Post on October 28 blamed Trump for both the synagogue shooting and the mail bombs, proclaiming, in a news headline, that "Trump, allies set the tone for the violence they denounce, critics say".
Almost all of the other targets who were intended recipients of packages also turn up in derogatory or highly critical tweets, including Hillary Clinton, Eric Holder and Maxine Waters. The newspaper appears to suggest, without saying outright, that Trump's criticism of his opponents fueled Sayoc's mail-bombing spree.
After Sayoc was taken into custody, the Federal Bureau of Investigation confirmed they found another package on Friday evening.More news: OnePlus 6T: All Specs Leaked
When asked why Sayoc had sent the bombs to Democrats, Sessions said that he was not sure, but added that the suspect "appears to be a partisan".
He said Sayoc had been talking about politics to everybody at the club for the last two weeks, preaching the need to elect Republicans during the November elections.
Speaking to reporters on Friday, the president said he knows the pipe bomb suspect was a supporter, but he bears "no blame" for his actions.
Ritchie reported the tweet immediately and blocked Sayoc. They declined to comment until after the hearing. The profile, under Cesar Altieri, describes experience as a booker and promoter of burlesque and Chippendale's shows. The company did eventually suspend Sayoc's account, but it wasn't until after he'd been arrested.
Friday night, Federal Bureau of Investigation agents questioned a person at a Broward County residence with a potential connection to Sayoc, but nothing came of the interview, according to law enforcement sources familiar with the probe.
The attorney was tapped by Sayoc's family because he has represented Sayoc multiple times in the past, including a 2002 arrest for threatening to blow up Florida Power & Light, saying "it would be worse than September 11".
His former boss Debra Gureghian, who manages New River Pizza in Fort Lauderdale, said she didn't think this would happen.
"He had that look of, 'I'm done, I surrender, '" Fiori said.