Arturo Palomino slapped down a domino during a game set up beside his lonely stall at a bus station in the Mexican capital.

“If I had Donald Trump in front of me, I would call him a racist imbecile,” the pirated DVD salesman said. “He thinks that because he has money he can say anything he likes.”

Nearly three weeks after the business tycoon announced his candidacy to be US president with a speech in which he claimed Mexican immigrants were criminals whose presence was undermining American greatness, the row refuses to die.

“When Mexico sends its people, they’re not sending the best,” Trump said during the announcement on 16 June. “They’re bringing drugs, they’re bringing crime. They’re rapists and some, I assume, are good people.”

Outrage has been widespread among the Mexican people, from those struggling to make a living on the streets to some of the richest businessmen in the world. In a country fraught with divisions over how to create the jobs and security necessary to make mass migration unnecessary, opposition to Trump’s remarks has provided rare unity.

“If you offend us we come together, and what he said was very offensive. He has no respect for human beings,” said Rita Hernández, sitting beside her stall, from which she sold brooms.

“We have a lot of problems in our country and they hurt us a lot, but the migrants who go to the US are hardworking people looking for a way to support their families, and when American tourists come here we treat them with warmth.”

Powerful Mexicans have sought to identify with such sentiments, severing business ties with the magnate and the Miss Universe pageant he owns. The TV giant Televisa said it was cutting all ties with Trump companies and would not be airing Miss Universe, in which he has a stake. The TV network Ora, owned by the telecommunications magnate Carlos Slim, announced it was also boycotting Trump and his competition.

Mexican expressions of disgust over Trump’s bigotry have frequently been laced with pot shots at his appearance. Former actress Carmen Salinas, recently elected as a federal deputy, released a YouTube video urging the business mogul and reality TV star to recognise that he had “the face of a dried-up louse”.

Piñata maker Dalton Ramirez said a new model – with a shock of blond hair and a big mouth – was proving particularly popular.

Bitter humour is, some say, the only recourse they have. Mauro Tlatengo recalled the 10 years he spent picking grapes, tending golf courses and working construction in California, Pennsylvania and New York, before returning to Mexico voluntarily because he missed his country. Trump’s comments made him angry but mostly, he said, they made him feel powerless.

“He is a crazy idiot who we can’t do anything about,” Tlatengo said. “But we can laugh at him.”

The comedian and filmmaker Eugenio Derbez tapped into this feeling while accepting an award in Los Angeles.

“You are wrong, Mr Trump. We are honest and hardworking people,” he said. “We are also waiters and cooks in all the restaurants of the United States. So take care the next time you eat at a restaurant, because it is possible that you might have to eat your words … and something else.”

Donald Trump speaks at his campaign launch, in New York City in June. Photograph: Richard Drew/AP

Trump has drawn fire from other Latin American countries. The reigning Miss Universe, Paulina Vega of Colombia, said his comments “were hurtful and unfair”, while Costa Rica announced it would not be sending a contestant to this year’s pageant.

Venezuelan president Nicolás Maduro joined the fray with two televised messages. “He who messes with Mexico messes with Venezuela,” he said in the first.

Trump has been unrepentant, apparently lapping up the publicity his comments have brought to his campaign, in which polls show him surging in the Republican field as other candidates are more wary of alienating the Latino vote.

In an interview on Fox News this weekend, he brushed off the decisions by NBC and Univision not to air Miss Universe, as well as the announcement that Macy’s was dropping a clothing line, that New York would review his contracts with the city, and that Nascar was moving its annual banquet from a resort he owns in Miami.

“The crime is raging, it’s raging, and it’s violent,” he said. “And if you talk about it, you’re a racist. I don’t understand it.

“It seems I am a whipping post for bringing it up.”