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Paulo Carreno, Mexican deputy foreign minister in charge of North America, gestures during an interview in Mexico City, June 9, 2016. REUTERS/EDGARD GARRIDO

Mexico has increased dialogue with American companies to make the case for bilateral economic ties, a senior official said on Thursday, in an effort to counter anti-Mexican rhetoric in the U.S. presidential campaign.

Presumptive Republican nominee Donald Trump has said Mexico is "killing" U.S. trade, threatening to build a border wall to keep out migrants, block remittances sent home by Mexicans, and raise tariffs against Mexico to protect U.S. jobs.

While generally at pains to avoid addressing Trump directly, Mexican government officials have warned that his proposals could do serious damage to both nations' economies.

Paulo Carreno, Mexico's new deputy foreign minister responsible for North America, was appointed in April to lead a drive to bolster his country's standing in the United States.

Since then, Mexico's diplomatic network in the United States has stepped up efforts to reach out to business leaders, as well as politicians and academics, Carreno said, keen to stress that his government took no side in the presidential contest.

Of the companies Mexico had met, the majority agreed with a model of bilateral economic cooperation based on free trade that did not involve a border wall, or protective tariffs, he said.

"They understand the benefit of greater commercial integration, and they live from it in a way," said Carreno. "They agree that the model we have today is the better one, though of course that's not to say it can't be improved."

U.S.-Mexico trade is worth some $500 billion every year and the U.S. Chamber of Commerce says roughly 6 million American jobs depend on it. In addition, an estimated 35 million people in the United States are Mexican or of Mexican background.

Mexican business leaders say U.S. companies are crucial allies in their battle to counter Trump's arguments.

Carreno did not detail which companies Mexico was meeting, though senior officials have said previously that those with major operations south of the border are key interlocutors.

They include firms like General Electric as well as carmakers General Motors and Ford. Both carmakers have been attacked by Trump in the campaign for investing in Mexico.