Agents tried to question him immediately, according to one law enforcement official.
He said Trump has instead gone to Washington and just plundered away.
Trump told reporters Friday afternoon that he was aware that the suspect was a supporter of his, but that he bore "no blame" for his actions.
The Department of Homeland Security has said there are no links to global terrorism.
Texas Democratic strategist Jason Stanford said that Trump's harsh rhetoric against Democrats was a motivating factor for the suspect, "His words have consequences", he said.
Although Sayoc is in custody, Federal Bureau of Investigation director Wray cautioned that there could be more potential explosive devices sent that have yet to be detected. "We will not tolerate such lawlessness, especially not political violence", said Sessions. "Let this be a lesson to anyone, regardless of their political beliefs, that we will bring the full force of law against anyone who attempts to use threats, intimidation and outright violence to further an agenda". CNN received one of the suspicious packages at its NY office.
FBI Director Christopher Wray told the news conference that fingerprints on a package sent to Representative Maxine Waters belonged to Sayoc.
Earlier Friday, authorities arrested 56-year-old Cesar Sayoc in connection with the packages.
The Seminole Tribe of Florida, which owns the casino, said it could find no evidence that Sayoc worked there, but added it could not verify whether he was an employee of a vendor company. With that, authorities began zeroing in on Sayoc on Thursday, gathering mobile phone records to track his past movements and conducting real-time surveillance of his location and activities, the official said. "They may have paid him to do it". But he said they did contain potentially explosive material, adding: "These are not hoax devices".
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On Wednesday, a suspicious package was sent to the office of Wasserman Schultz hours after other top Democrats, including Hillary Clinton, former Vice President Joe Biden and former President Barack Obama, were also sent crude pipe bombs.
An earlier package had been sent to former Obama CIA Director John Brennan in care of CNN in NY.
All the people targeted by the suspicious packages have often been maligned by right-wing critics.
The targets of the bombing spree were all prominent Trump critics. On both the packages and the social media posts, her name was spelt "Shultz", according to the complaint.
The complaint accused Sayoc of sending 13 bombs to 11 individuals, starting with billionaire Democratic donor George Soros.
Sayoc is a Republican who registered to vote in 2016.
In May 2014, he pleaded guilty to charges of grand theft and battery arising from a shoplifting arrest at Macy's department store, court documents indicate.
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 bound to enrage his opponents.
Asked on Friday about pro-Trump stickers or signs on the van allegedly driven by the suspect, Trump said: "I did not see my face on the van".
"I'm hoping you think it's wrong to hear people spend years, months, vilifying people, questioning their patriotism, calling them enemies of the people - and then suddenly you're concerned about civility".