"The bottom line is that Americans must unify," Trump said. "We must show the world that we are united together in peace and love and harmony as fellow American citizens. There is no country like our country."
Cesar Sayoc, 56, of Aventura, Florida, was taken into custody earlier in the day and is expected to face federal criminal charges in the matter, according to NBC News.
The president said he instructed authorities to spare no expense in prosecuting "them, him, her, whoever it may be to the fullest extent of the law." The remark prompted laughter from the audience.
"These terrorizing acts are despicable and have no place in our country," Trump said.
The president did not mention Sayoc by name Friday. The Justice Department said that more information would be made available at an afternoon news conference.
Trump congratulated law enforcement for doing an "incredible, incredible job."
"I want to applaud the FBI, Secret Service, the Department of Justice, the U.S. Attorney's Office for the Southern District of New York, the NYPD and all law enforcement throughout the entire country, incredible partners," Trump said. "These people have worked so hard. And to have done it so quickly. It's looking like a needle in a haystack, how do you do this so quickly."
Shortly after the president's comments promoting unity, he criticized "globalists," who he said were cheating American workers. The remark prompted shouts of "Soros" and "Lock him up!" from the audience. In response, Trump pointed to the crowd and repeated: "Lock him up."
Earlier in the day, the president tied the mail bombs to efforts to hamstring Republican electoral chances.
Trump said in a Friday Twitter post that "now this 'Bomb' stuff" threatened to slow GOP momentum headed into the midterms next month. On Thursday, he blamed the "purposely false and inaccurate reporting of the Mainstream Media that I refer to as Fake News" for increasing levels of anger in society.
The devices were sent to some of Trump's most vocal critics, including the liberal billionaire George Soros, former presidential contender Hillary Clinton, and former President Barack Obama. Another device was addressed to Obama's CIA director John Brennan, care of CNN.
The targets include those who have faced the president's harshest attacks on the campaign trail and at his rallies as president.
On Friday, law enforcement officials said two more devices had been intercepted, addressed to former Director of National Intelligence James Clapper, also via CNN, and to Sen. Cory Booker, D-N.J.
The president was speaking Friday at a Young Black Leadership Summit at the White House.