US President Donald Trump has urged Americans to “condemn racism, bigotry and white supremacy” after 31 people were killed in mass shootings in Texas and Ohio.

Avoiding the sensitive subject of gun law reform, the president talked up the death penalty for mass murderers and perpetrators of hate crimes, as well as tougher mental health laws to better identify mentally ill individuals.

“Mental illness and hatred pulls the trigger, not the gun,” Mr Trump said at The White House on Monday.

The death toll from Saturday’s mass shooting at a shopping centre in El Paso, Texas initially stood at 20, but has risen to 22 after two more victims died in hospital.

Texas man Patrick Crusius, 21, faces the death penalty after being charged with murder over the shootings.

He is also being investigated for hate crimes after it emerged he posted racist online rants praising the Christchurch massacre and white supremacy.

In a separate mass shooting just 13 hours later in Dayton, Ohio, 24-year-old Connor Betts fatally shot nine people – including his 22-year-old sister.

Former classmates of Betts have spoken up about the killer, calling him a “bully” who frequently threatened violence against women.

People who knew Connor Betts in high school have described the killer as a bully. Photo: Facebook

Women have spoken up about feeling scared of Connor Betts. Photo: Twitter

Among his policy options in response to the shootings, Mr Trump also directed the Department of Justice to work with local authorities and social media companies to detect mass shooters before they strike.

He said Americans needed to stop glorifying violence in society, and pointed to “gruesome and grisly” video games.

“It is too easy today for troubled youth to surround themselves with a culture that celebrates violence,” Mr Trump said.

“We must stop or substantially reduce this and it has to begin immediately.”

He did not mention his own anti-immigration “invasion” rhetoric, which includes describing migrants from Central and South America as criminals, gang members and rapists.

Many Gang Members and some very bad people are mixed into the Caravan heading to our Southern Border. Please go back, you will not be admitted into the United States unless you go through the legal process. This is an invasion of our Country and our Military is waiting for you!

— Donald J. Trump (@realDonaldTrump) October 29, 2018

“Hate has no place in America – hatred warps the mind, ravages the heart and devours the soul,” Mr Trump said.

“We must make sure those judged to pose a grave risk to public safety do not have access to firearms and that if they do those firearms can be taken through rapid due process.”

Earlier on Monday, Trump had urged lawmakers in a tweet to put strong checks in place on potential gun buyers, suggesting action could be tied with immigration reform.

In his remarks at the White House, however, he did not mention immigration.

Democrats, who have long pushed for greater gun control, said Mr Trump was indirectly to blame for the attack in Texas, with some drawing connections between his rhetoric to a resurgence in nationalism and xenophobic sentiment.

-with AAP