Taken into custody after a firefight with police, the suspect was transferred to hospital.
Federal prosecutors filed 29 charges on Saturday evening against the man suspected of fatally shooting at least 11 people at a synagogue in Pittsburgh, Pennsylvania.
Former presidents Barack Obama and Bill Clinton as well as former first lady, Hillary Clinton, also joined to condemn the massacre, described as among the deadliest against the Jewish community in the U.S.
"We must stand with our Jewish brothers and sisters to defeat anti-Semitism and vanquish the forces of hate". Trump said that he felt "obligated" to hold the event, despite the tragedy in Pittsburgh.
Trump also called for the death penalty, and he said the shooting looks "definitely like it's an anti-Semitic crime, and that is something you wouldn't believe could still be going on".
An ambulance arrives at the Tree of Life Synagogue where a shooter opened fire Saturday.
Communities across the United States held ad-hoc vigils over the weekend to mourn those who were killed by Bowers, and more are planned for the week. "I recognized it as gunshots".
Authorities said Bowers was armed with an assault rifle and at least three handguns when he burst into the Tree of Life synagogue. "It's one of the worst that I've seen".
"We commend the Pittsburgh police department for responding so quickly to this terrifying situation and preventing further casualties, and for effectively apprehending the assailant", Lauder said. No children were among the casualties.
In his statement, Mr Obama said: "We grieve for the Americans murdered in Pittsburgh".
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Bowers, who the Federal Bureau of Investigation said was not previously known to law enforcement, appeared to be the author of a rash of anti-Semitic online posts, notably on the Gab.com website, where conspiracy theories are common.
Trump had initially called for unity in the face of Saturday's assault on the Tree of Life synagogue in Pittsburgh, in a week in which prominent Democrats were the targets of pipe bombs sent through the mail, allegedly by a Trump supporter in Florida.
"Ultimately, it's about respecting and understanding diversity, and that we all come from different places, yet we're all Americans, and we're all citizens of this country, and we all have equal opportunities to be respected in that way", Hermanson added.
Israeli Prime Minister Benjamin Netanyahu said he was "heartbroken and appalled" by the attack.