"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."