"I am pleased to inform you that law enforcement has apprehended the suspect and taken him into custody. Incredible job by law enforcement," Trump said at a White House event for young black leaders on Friday.
"These terrorizing acts are despicable and have no place in our country," he said.
"We will prosecute them, him, her, whoever it may be, to the fullest extent of the law," Trump added. "We must never allow political violence to take root in America."
Later at the same event, Trump referenced the investigation, saying that his announcement on drug prices was "competing with the story that took place."
There were sporadic shouts of "fake news," "CNN sucks" and "Soros" from individuals in the crowd at the event, which is not uncommon for Trump campaign rallies but more unusual from inside the White House.
Trump's comment about the news coverage was the second time in several hours that Trump appeared to complain about the focus of media coverage about the investigation into the suspected package bombs that were addressed to a series of high profile individuals and Democratic politicians.
Friday morning, Trump tweeted his concerns that media's coverage of the ongoing bomb crisis has been overshadowing the midterm elections, even as his staff insisted he has been "receiving constant information" about the ongoing security situation.
"Republicans are doing so well in early voting, and at the polls, and now this “Bomb” stuff happens and the momentum greatly slows - news not talking politics. Very unfortunate, what is going on. Republicans, go out and vote!" Trump tweeted at 10:19 a.m. Friday.
Earlier this morning, the president wrote a half-sentence tweet criticizing CNN, deleted it, then wrote a full tweet criticizing CNN "and others" the same week the television network was mailed a bomb.
"Funny how lowly rated CNN, and others, can criticize me at will, even blaming me for the current spate of Bombs ... yet when I criticize them they go wild and scream, 'it's just not Presidential!'" Trump tweeted at 3:14 a.m. Friday morning.
At 2:48 a.m., he'd tweeted: "Funny how lowly rated CNN and others can criticize."
That tweet was quickly deleted, but ABC News obtained a screengrab.
This comes after Trump, at a rally earlier this week, bragged about "how nice I'm behaving tonight."
In addition to former President Barack Obama and former Secretary of State Hillary Clinton, other politicians who were addressed in the various packages include former Vice President Joe Biden, former Attorney General Eric Holder, Rep. Maxine Waters, and Sen. Cory Booker.
Democratic donor George Soros and actor Robert De Niro, who was critical of the commander in chief at this year's Academy Awards, were also the targets of suspicious packages.
During an introduction of Bruce Springsteen, De Niro said: "First, I wanna say, 'F--k Trump. It's no longer, 'Down with Trump,' it's 'F--k Trump.'"
The president responded by calling the two-time Oscar winner "a very Low IQ individual."
To date, 13 suspicious packages believed to have explosive devices have been found in various locations across the country, all addressed to high-profile Democratic politicians or public figures who have been open in expressing their criticism of the Trump administration.