The Squirrel Hill area was home to the late Fred Rogers whose long-running children's television show Mr Rogers Neighborhood featured lessons on friendship and kindness.
The Hill has reached out to the Islamic Center of Pittsburgh for comment.
In a statement, Dayton called the shooting "a hateful act of violence committed against the Jewish community".
Calling the shooting an "evil anti-Semitic attack", Trump ordered flags at federal buildings throughout the USA to be flown at half-staff in honor of the victims.
"If they had some kind of a protection inside the temple maybe it could have been a much more different situation, they didn't", he said when asked if there was any link to United States gun laws.
"I've heard the president's comments about how we should arm guards in our synagogues, our churches, our mosques. He gets up in the morning with new and inventive ways to divide us", US Representative Adam Schiff, a California Democrat who is Jewish, said on CNN's "State of the Union" broadcast on Sunday.
The six people injured included four police officers, one of whom was released later Saturday and another "we are praying will be released today", Pittsburgh Police Chief Scott Schubert said.
Trump also told reporters he planned to travel to Pittsburgh this week.
David and Cecil Rosenthal, aged 54 and 59 respectively, were identified as the brothers who were killed.
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While some acknowledged the political undertones of the gathering, many, including 45-year-old Ira Piltz, said they were heartened to see such a large crowd come out to show their support for the Jewish community.
They joined religious leaders across all faiths at a vigil on Sunday in the honour of the victims of the shooting.
Mr Jones said Mr Bowers was armed with an assault rifle and three handguns.
A tactical team found Bowers on the third floor, where he shot two officers multiple times, an affidavit said.
Bowers has been arrested and is being treated for gunshot wounds at a hospital. She said she thinks more synagogues will hire security and lock their doors in the wake of the Pittsburgh attack.
The Department of Justice charged the suspect with 11 counts of criminal homicide, and 13 counts of ethnic intimidation.
Bowers had made many anti-Semitic posts online, including one early on Saturday. "Screw your optics, I'm going in", Bowers had posted in what appears to be his last post on "Gab", a social media site popular with the alt-right.
The emerging evidence strongly suggests that the attack was motivated by anti-Semitism and was the deadliest against the Jewish community in the history of the USA, as per the Anti Defamation League, a Jewish non-governmental organisation.
In Israel, cabinet ministers stood for a moment of silence on Sunday to honor the victims of the shooting.