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Donald Trump’s anti-migrant rhetoric has stoked racism in the United States and led directly to increased violence such as the mass shooting in El Paso on Saturday that left at least 20 people dead, according to Democratic presidential candidate Beto O’Rourke.

As police investigated the possibility that the gun rampage in the Texas city was a hate crime aimed at Latino immigrants, O’Rourke accused the president of being a “racist” who was trying to make Americans “afraid” of migrants.

There was a link between Trump’s hostile comments about Muslims, migrants and people of colour to a rise in hate crimes, O’Rourke told CNN after cutting short campaigning in Nevada to return to El Paso, his hometown and a city he represented for six years in Congress.

Asked if the shooting was Trump’s fault for inflaming hatred, he said “yes”.

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“We’ve had a rise in hate crimes every single one of the last three years during an administration where you have a president who has called Mexicans rapists and criminals, though Mexican immigrants commit crimes at a far lower rate than people born in this country.

“He has tried to make us afraid of them … attempting to ban all Muslims from this country. The day that he signed that executive order the mosque in Victoria, Texas was burned to the ground. Those chants that we heard in Greenville North Carolina – ‘send her back’ – talking about fellow American citizens duly elected to represent their constituents in Congress …

“He is a racist. He is stoking racism in this country ... and it fundamentally changes the character of the country and leads to violence.”

El Paso police chief Greg Allen said on Saturday night that authorities were examining a manifesto from the suspect and said “there is a potential nexus to a hate crime”. But officials declined to elaborate and said the investigation was continuing.

But a four-page statement posted on 8chan, an online message board often used by extremists, and believed to have been authored by the suspect, called the Walmart attack “a response to the Hispanic invasion of Texas”.

O’Rourke, who said he was proud of the way El Pasoans were “standing up” for the victims of the shooting, also said more effort must be made to bring about reform of the country’s gun laws.

“We must make sure that we change our laws so we make it harder for this to happen again. We must ask ourselves about the level of hatred and racism that we’re seeing in this country right now that could lead to an event like we saw here today and that’s on all of us to call out and stop.”

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Speaking in Las Vegas earlier, O’Rourke said the US may require direct action, urgency and in some cases nonviolent civil disobedience, to make real change.

“I believe in this country. I believe, at the end of the day, we’re going to be able to get this done,” he said, “but it’s going to be because of those people who force it to get done.”

One of Texas’ current Democratic members of Congress also linked the shooting to Trump’s racist rhetoric.

The El Paso shooting was “an act of terrorism against Hispanic Americans,” Rep. Joaquin Castro, a Texas Democratic congressman and the twin brother of 2020 Democratic presidential candidate Julián Castro, tweeted on Saturday.

“The language in the shooter’s manifesto is consistent with President Trump’s description of Hispanic immigrants as ‘invaders.’ Today’s shooting is a stark reminder of the dangers of such rhetoric.”

The alleged “manifesto” described a shooting attack designed as “a response to the Hispanic invasion of Texas”.

Bernie Sanders, who was with O’Rourke and 17 other Democratic hopefuls to address a union meeting in Las Vegas earlier on Saturday, said: “It’s not just today, it has happened several times this week. It’s happened here in Las Vegas where some lunatic killed some 50 odd people,”the Vermont senator said.

“All over the world, people are looking at the United States and wondering what is going on? What is the mental health situation in America, where time after time, after time, after time, we’re seeing indescribable horror.”

Sanders blasted Republican Senate leadership for being more concerned about pleasing the gun lobby than “listening to the vast majority of the American people” . He said Trump had a responsibility to support commonsense gun safety legislation.

California senator Kamala Harris promised to use an executive action within her first 100 days of taking office to impose gun control while New Jersey senator Cory Booker said: “This has got to be a movement, politics or not, we’ve got to make ending this nightmare a movement before it happens to yet another community or another person dies.”

Joe Biden said the gun violence was “beyond anything that we should be tolerating”. He added: “We can beat the NRA. We can beat the gun manufacturers.”

Shortly after the shooting and before its death toll was widely reported, White House officials said Trump had been briefed while spending the weekend at his New Jersey golf club. He conveyed his initial reaction on Twitter, writing that the shooting was “terrible” and that he was in close consultation with state officials.

Later Saturday night, Trump tweeted condolences. “Today’s shooting in El Paso, Texas was not only tragic, it was an act of cowardice. I know that I stand with everyone in this Country to condemn today’s hateful act. There are no reasons or excuses that will ever justify killing innocent people. Melania and I send our heartfelt thoughts and prayers to the great people of Texas.”