DAYTON, Ohio -- Dayton Mayor Nan Whaley's stricken community will have a visitor Wednesday in President Donald Trump, who in the wake of two mass shootings over the weekend has made calls for unity on the heels of his divisive political talk.

White House officials said Trump's visits to Texas and Ohio, where a combined 31 people were killed and dozens wounded in less than 24 hours, would be similar to those he's paid to grieving communities in the past. But Whaley, a Democrat, made remarks Tuesday questioning whether the visit will help, and expressed disappointment in the president's aftermath remarks that included an erroneous reference to Toledo instead of Dayton.

"I can only hope that as president of the United States that he's coming here because he wants to add value to our community and he recognizes that that's what our community needs," she said, noting that she expected to meet with Trump. "Everyone has it in their power to be a force to bring people together, and everybody has it in their power to be a force to bring people apart -- that's up to the president of the United States."

Connor Betts, 24, opened fire in Dayton's Oregon entertainment district early Sunday morning, killing nine people including his 22-year-old sister, before officers fatally shot him within 30 seconds of the start of his rampage. The FBI announced Tuesday it's opened an investigation into Betts' desire to commit a mass shooting and his interest in violent ideology.

GOP Gov. Mike DeWine said it's clear Betts exhibited anti-social behaviours in high school that should have alerted those around him to a problem. Two former classmates told The Associated Press that Betts was suspended from Bellbrook High School after a hit list was found scrawled in a school bathroom. That followed an earlier suspension after Betts came to school with a list of female students he wanted to sexually assault, according to the two classmates, a man and a woman who spoke on condition of anonymity out of concern they might face harassment.

But Betts had no apparent criminal record as an adult, and police said there was nothing that would have prevented him from buying a gun.

DeWine on Tuesday called on the Republican-led Legislature to pass laws requiring background checks for nearly all gun sales, allowing courts to restrict firearms access for people perceived as threats, and improving access to in-patient psychiatric care for those who need it most.

"If we, after a tragedy, only confine ourselves to doing those things that would have prevented this tragedy, we are missing a real opportunity," DeWine said. "So we need to look at these tragedies together."

Trump himself said Monday he might call for more stringent background checks if such a measure could be paired with immigration reform, although he did not offer specifics.

Special Agent Todd Wickerham, who announced the FBI investigation, didn't say if agents are looking at whether the Dayton shooting should be treated as domestic terrorism, as the agency has done in the recent El Paso, Texas, and Gilroy, California, shootings. He said Betts hadn't been on the FBI's radar.

Meanwhile, a woman who said she briefly dated Betts spoke to reporters Tuesday and wrote an online essay, saying the two bonded over struggles with mental illness.

Adelia Johnson, 24, said they met in a college psychology class. Johnson said she was in treatment but that Betts "didn't want to seek help because of the stigma." He told her he thought he had mental illnesses including bipolar disorder, she said.

"When he started joking about his dark thoughts, I understood," she wrote. "Dark thoughts for someone with a mental illness are just a symptom that we have to learn how to manage."

Johnson said on their first date, Betts showed her a video of last October's Pittsburgh synagogue shooting in which a man shouting anti-Semitic slurs opened fire and killed 11 people.

The family of Betts and his sister, Megan Betts, released a statement through police Tuesday night, saying they are devastated and co-operating with law enforcement's investigation.

It's unknown whether any of the Dayton victims were targeted. Besides Megan Betts, 22, the others who died were Monica Brickhouse, 39; Nicholas Cumer, 25; Derrick Fudge, 57; Thomas McNichols, 25; Lois Oglesby, 27; Saeed Saleh, 38; Logan Turner, 30; and Beatrice N. Warren-Curtis, 36.

Betts was white and six of the nine killed were black, but police said the speed of the rampage made any discrimination in the shooting seem unlikely.

Hospital officials said 37 people have been treated for injuries, including 14 with gunshot wounds.

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Franko reported from Columbus. Associated Press writers Dan Sewell in Cincinnati, Julie Carr Smyth in Columbus, Amanda Seitz in Chicago and Robert Bumsted in Dayton contributed.