Dayton police have discovered evidence that the gunman who opened fire in a the city's entertainment district early Sunday had "a history of obsession with violent ideations," including mass shootings, and had expressed "a desire to commit a mass shooting."

But Chief Richard Biehl said Tuesday there is still no clear motive for the shooting.

The FBI has now opened an investigation into the attack, which left nine people, including the gunman's sister, dead.

Todd Wickerham, the FBI's special agent in charge of the Cincinnati field office, told reporters Tuesday the agency is working to figure out three things: "What, if any, ideology influenced the attacker to conduct this attack. Who, if anyone, helped him or had any knowledge of his intentions to conduct this attack, and why he committed this specific act of violence."

Wickerham gave no details about the evidence but added: "We have not found any indication of racial motivation at this time."

The FBI has taken a central role in the investigation and say there is not yet a clear motive for the attack. (John Minchillo/The Associated Press)

Connor Betts, 24, was wearing a mask and body armour when he opened fire with an AR-15 style gun outside a strip of nightclubs. He killed his younger sister and eight others before officers fatally shot him less than 30 seconds into his rampage.

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

"The Betts family would like to express their enormous gratitude and love for everyone that has reached out and given their support during this awful time," the statement reads. "They ask that everyone respect the family's privacy in order to mourn the loss of their son and daughter and to process the horror of Sunday's events."

Facing pressure to take action after the latest mass shooting in the U.S., Ohio's Republican governor urged the state legislature to pass laws requiring background checks for nearly all gun sales and allowing courts to restrict firearms access for people perceived as threats.

Gov. Mike DeWine said during a news conference Tuesday that Ohio needs to do more while balancing people's rights to own firearms and have due process. He outlined a series of legislative actions he wants the legislature, led by Republicans, to take up to address mental health and gun violence.

"We can come together to do these things to save lives," DeWine said.

Protesters once again shouted "Do something!" — a refrain chanted during Sunday's vigil honouring the victims — at DeWine at the start of his Tuesday announcement. One person yelled "Shame on you!" at DeWine while he was answering questions.

His calls for action could be an uphill battle for the legislature, which has given little consideration this session to those and other gun-safety measures already introduced by Democrats. DeWine's Republican predecessor, John Kasich, also unsuccessfully pushed for a so-called red flag law on restricting firearms for people considered threats.

DeWine said he has talked with legislative leaders and believes his proposals can pass.

This past weekend saw two back-to-back mass shootings in the United States: one in El Paso, Texas, and one in Dayton, Ohio. At least thirty-one people are dead. Dozens more injured. Today on Front Burner, we talk to writer Jennifer Mascia about gun violence and reform in America. She’s a reporter with The Trace, a non-profit, non-partisan organization dedicated to covering gun-related news. 25:49

Dayton Mayor Nan Whaley went further later in her comments to reporters, saying she has long been in favour of a ban on assault weapons.

"The issue is if [the shooter] didn't have a gun like that, we wouldn't see so much fast death that happened in 30 seconds, and I shared that with the president when he called me Sunday evening."

One day before U.S. President Donald Trump's scheduled visit to Dayton, Whaley said she has been disappointed with his remarks in the wake of the shooting, noting he only mentioned gun issues once.

"I don't know if he knows what he believes, quite frankly," the mayor said.

Ohio Gov. Mike DeWine will try to succeed where his predecessor, John Kasich, was unable with respect to a so-called red flag law. (Paul Vernon/The Associated Press)

Police say nothing in the Dayton shooter's background prevented him from buying the firearm used.

The shooting outside a strip of nightclubs early Sunday and another mass shooting in El Paso, Texas, during the past weekend left a combined total of 31 people dead and more than 50 injured in less than 24 hours.

Betts had no apparent criminal record as an adult, and police said there was nothing that would have prevented him from buying a gun. Ohio law bars anyone convicted of a felony as an adult, or convicted of a juvenile charge that would have been a felony if they were 18 or older, from buying firearms.

Two former classmates told The Associated Press that Betts was suspended during their junior year at 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 are both now 24 and spoke on condition of anonymity out of concern they might face harassment.

Bellbrook-Sugarcreek Schools wouldn't comment and refused to release information about Betts, citing legal protections for student records.

Bellbrook police Chief Doug Doherty said he and his officers had no previous contact with Betts and weren't aware of any history of violence. Sugarcreek Township police said the only records they have on Betts are from a 2015 traffic citation. They noted without further explanation that Ohio law allows sealed juvenile court records to be expunged after five years or when the person involved turns 23.

New details are emerging in a mass shooting in Dayton, Ohio Sunday, though the gunman’s motive remains a mystery. 1:29

Still unknown is whether Betts targeted any of the victims, which included his sister, Megan, 22.

"It seems to just defy believability he would shoot his own sister, but it's also hard to believe that he didn't recognize it was his sister, so we just don't know," Biehl said.

Authorities identified the others who were killed as:

Monica Brickhouse, 39.

Nicholas Cumer, 25.

Derrick Fudge, 57.

Thomas McNichols, 25.

Lois Oglesby, 27.

Saeed Saleh, 38.

Logan Turner, 30.

Beatrice N. Warren-Curtis, 36.

Of the more than 30 people injured in Ohio, at least 14 had gunshot wounds; others were hurt as people fled, city officials said. Eleven remained hospitalized Monday, Fire Chief Jeffrey Payne said.

While the gunman was white and six of the nine killed were black, police said the speed of the rampage made any discrimination in the shooting seem unlikely. It all happened within 30 seconds, before police officers stationed nearby fatally shot Betts.

Trump said Monday he wanted Washington to "come together" on legislation providing "strong background checks" for gun users, but he gave no details. Previous gun control measures have languished in the Republican-controlled Senate, including a bill passed by the Democrat-led House that includes fixes to the nation's firearm background check system.