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Falco released the statement in response to an incident that occurred during a press conference on Tuesday between Trump and Univision news anchor Jorge Ramos.
During the conference, Ramos repeatedly attempted to question Trump's controversial plans for immigration reform, but was unceremoniously cut off and escorted out of the room.
Trump and Univision, the biggest Spanish-language network in the US, have been at odds for much of Trump's months-long presidential campaign.
Falco warned that Trump "is going to get tough questions from the press and has to answer them," and scolded the candidate for treating Ramos, a renowned news veteran, with "disregard for him and for the countless Hispanics whom Jorge seeks to represent through press questions that are at the heart of the First Amendment."
Trump and Falco have been at war ever since Trump's campaign announcement in June, during which he used unsavory language to describe Mexican immigrants. Since then, the network has bowed out of any further coverage of the Miss USA pageant, to which Trump responded with a lawsuit.
Though the Republican candidate has so far avoided any meaningful backlash over his controversial statements, his confrontation with Ramos Tuesday night was widely seen as a potentially damning mistake because Ramos, who works for both Fusion and Univision, has the ear of millions of Hispanic viewers.
Nielsen data cited by the Los Angeles Times show the news program, "Noticiero Univison," which Ramos has anchored since 1986, boasts 2 million viewers per night.
You can read Falco's full statement below:
The recent treatment that Jorge Ramos received at Mr. Trump's press conference in Iowa is beneath contempt. As a Presidential candidate, Mr. Trump is going to get tough questions from the press and has to answer them. Jorge Ramos is one of the most professional, dedicated and respected journalists I have seen or worked with in my 40 years in media. He always asks hard questions of candidates and elected officials, regardless of party or issue. Mr. Trump demonstrated complete disregard for him and for the countless Hispanics whom Jorge seeks to represent through press questions that are at the heart of the First Amendment. I remain grateful for the first-rate journalistic work that Jorge and all of his news colleagues at Univision and Fusion do to bring all points of view to the 57 million Hispanics in this country.