President Trump on Monday denounced “racism, bigotry and white supremacy” after a pair of mass shootings and focused on combating mental illness over efforts to push gun control.

Trump’s nationally televised comments followed a shooting rampage on Saturday in El Paso, and another, hours later, in Dayton, Ohio, both with assault-style rifles and loads of ammunition. Thus far, 31 people have died as a result of the two attacks, with two more people who were shot in El Paso succumbing to their wounds on Monday. Scores of others were wounded.

“In one voice, our nation must condemn racism, bigotry and white supremacy,” Trump said in remarks delivered at the White House. “Hatred warps the mind, ravages the heart and devours the soul.”

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Trump condemned the “two evil attacks” and vowed to act “with urgent resolve,” outlining several possible steps, including the use of “red-flag laws” that focus on better identifying mentally ill people — and others who present as threats for violence — who should not be allowed to purchase firearms.

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“Mental illness and hatred pull the trigger. Not the gun,” said Trump, who was accompanied by Vice President Pence and did not take questions from reporters. Trump also called for cultural changes, including stopping the “glorification of violence in our society” in video games and elsewhere.

Research has found no link between violent video games and shooting people, and studies of mass shooters have found that while some had mental-health issues, many did not, with other factors — including past domestic violence, a strong sense of resentment and a desire for infamy — emerging as stronger predictors.

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Hours earlier, on Twitter, he called for “strong background checks” and suggested pairing gun legislation with new immigration laws, a top priority of his administration that he has failed to move through Congress. Trump made a similar call to strengthen background checks after a mass shooting last year at a Florida school, and he has since threatened to veto bills passed by House Democrats seeking to do so. Trump did not mention background checks in his televised remarks.

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In his tweets, Trump said: “Republicans and Democrats must come together and get strong background checks, perhaps marrying this legislation with desperately needed immigration reform. We must have something good, if not GREAT, come out of these two tragic events!”

Trump also appeared to blame the media for recent mass shootings in a tweet on Monday, writing that “Fake News has contributed greatly to the anger and rage that has built up over many years.”

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Authorities are investigating the El Paso shooting, along the U.S. border, as a hate crime and domestic terrorism, and they are combing through a manifesto officials think the suspected attacker posted online that included anti-immigrant sentiments. The shooting occurred in a shopping area with a Walmart known to draw Mexican nationals from Juarez.

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The twin terrors in a span of hours over the weekend again horrified a nation that has become numb to the familiar and repetitive tragedies. They prompted, as usual, a push for stricter gun-control measures, debates over virulent rhetoric and anguish over the relentless stream of such attacks across the United States.

While admonishing people to condemn the ideologies that have spawned some of the nation’s worst mass shootings, Trump and his own commentary have been central aspects of the debate since El Paso. The president, who has staked much of his presidency on efforts to keep undocumented immigrants out of the country, has a history of denigrating them. He also has been criticized for his unwillingness to vilify white supremacists, such as in his response to the violent confrontation between white supremacists and counterprotesters in Charlottesville in 2017, after which he said there were “very fine people” on both sides.

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During his remarks, Trump said he was directing the Justice Department to propose legislation “ensuring that those who commit hate crimes and mass murders face the death penalty” and that this punishment be carried out rapidly and “without years of needless delay.”

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People convicted of carrying out such crimes already can face death sentences in many cases. In a recent example involving a mass killing fueled by racial hatred, federal prosecutors sought and won a death sentence for the avowed white supremacist convicted of killing nine black parishioners inside a Charleston, S.C., church in 2015.

Not long after Trump spoke, former president Barack Obama released a statement bluntly pushing back against what he called “language coming out of the mouths of any of our leaders that feeds a climate of fear and hatred or normalizes racist sentiments.”

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Obama did not mention Trump by name, but his statement appeared to be an implicit rebuke of his successor, denouncing “leaders who demonize those who don’t look like us” or those who suggest that immigrants “threaten our way of life.”

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He also called for new gun laws, saying that the country is “not helpless” in the face of the mass shootings that have become a regular feature in American society.

“Every time this happens, we’re told that tougher gun laws won’t stop all murders; that they won’t stop every deranged individual from getting a weapon and shooting innocent people in public places,” Obama said. “But the evidence shows that they can stop some killing. They can save some families from heartbreak.”

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Senate Majority Leader Mitch McConnell (R-Ky.) said Monday evening that Senate Republicans “are prepared to do our part.” He did not mention the word “gun” at any point in his statement.

The top two Democrats in Congress called on McConnell to bring the Senate back from recess to pass bills on background checks already approved by the House.

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“McConnell has called himself the ‘grim reaper’ and refuses to act on this bipartisan legislation,” House Speaker Nancy Pelosi (Calif.) and Senate Minority Leader Charles E. Schumer (N.Y.) said in a joint statement.

Pelosi and Schumer also chided Trump for not mentioning background checks in his televised remarks, suggesting that he was doing the bidding of the National Rifle Association.

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“It took less than three hours for the president to back off his call for stronger background check legislation,” Pelosi and Schumer said. “When he can’t mention guns while talking about gun violence, it shows the president remains prisoner to the gun lobby and the NRA.”

Federal officials have joined the investigations in both El Paso and Dayton. The FBI said it is assisting local police in Dayton, where authorities said Connor Betts, the 24-year-old gunman who opened fire in the city’s entertainment district, killed his sister during the attack.

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Richard S. Biehl, the Dayton police chief, said Monday that a motivation for that attack remained elusive. Unnerving glimpses of Betts’s background have emerged, including from an ex-girlfriend, who said he had worried that he might hurt people and described wrestling with hallucinations and hearing menacing voices.

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In El Paso, the FBI dispatched officials from a domestic terrorism-hate crimes fusion cell to investigate what John F. Bash, U.S. attorney for the Western District of Texas, called domestic terrorism. Bash said federal prosecutors are strongly weighing hate crimes and firearms charges against shooting suspect Patrick Crusius. Those charges could carry a death sentence.

The charges would not necessarily change the punishment handed down, as Crusius already faces a state capital murder charge, and prosecutors in El Paso say they will seek the death penalty.

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Crusius remains in jail after surrendering to police. Police say he has cooperated and answered questions, but they declined to elaborate.

“He basically appears to be in a state of shock and confusion,” Greg Allen, the El Paso police chief, said at a news briefing. Asked if the shooting suspect has shown remorse, Allen said: “No. Not to the investigators.”

Precise details of Crusius’s travels remained unclear Monday, but Allen said the suspected shooter spent between 10 and 11 hours traveling from Allen, Tex., to El Paso. After arriving, Allen said, he got lost in a neighborhood and then “found his way to the Walmart because, we understand, he was hungry.”

Crusius had lived with his grandparents in Allen until six weeks ago, the relatives said in a written statement, adding that they were “devastated” by the shooting.

According to court filings, he was remanded without bond early Sunday, and an attorney listed in court records said he had been appointed to represent Crusius but declined to comment.

Authorities in El Paso identified the victims on Monday; among them were people from at least three countries — the United States, Mexico and Germany — who ranged in age from 15 to 90. Their stories have provided heartbreaking glimpses of people killed while doing something mundane: shopping at Walmart.

Jordan and Andre Anchondo had gone to the store with their 2-month-old son. They were looking to buy birthday party decorations for their daughter, who was turning 6, and were going to have family and friends over to their new home for the first time, said Tito Anchondo, Andre’s brother.

Both of them were killed in the gunfire. Relatives think they died shielding their baby.

Alvaro Mena said Monday that his stepfather, Juan Velásquez, 78, had died earlier that morning. His mother was still hospitalized, Mena told reporters outside Del Sol Medical Center in El Paso.

The couple had been returning a window blind to Walmart and were shot in their car while parking, Mena said. They left Juarez several years ago seeking a safer city, choosing El Paso.

“That’s why they came here,” Mena said. “And they came for this? I just don’t have words for that.”

Eight of the shoppers killed in El Paso were Mexican. Mexico has expressed outrage at the massacre and suggested that it might try to bring charges against the perpetrator and the seller of the firearm.

Mexico’s foreign minister, Marcelo Ebrard, visited El Paso on Monday to meet with victims and their families and said that the Mexican attorney general would be opening a terrorism case against the shooter. He also said they would consider an extradition request given that some of those targeted were Mexicans.

“We agree with President Trump’s statement that racism and white supremacism are serious problems in the United States,” Ebrard said.

Eli Rosenberg, Scott Wilson and Robert Moore in El Paso; Mary Beth Sheridan and Gabriela Martinez in Mexico City; and Meagan Flynn, Hailey Fuchs, Hannah Natanson, Felicia Sonmez, Rebecca Tan and Matt Zapotosky in Washington contributed to this report.