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Donald J. Trump’s repeated threats against Mexico drew a forceful response on Monday from President Enrique Peña Nieto of Mexico, who vowed that his country would never pay for the Republican candidate’s much-ballyhooed border wall and warned that his language was reminiscent of Hitler and Mussolini.

Relations between the United States and Mexico have been somewhat strained in recent months as immigration has emerged as a central issue in the 2016 presidential campaign. Making his most direct comments to date about Mr. Trump, Mr. Peña Nieto acknowledged that the Manhattan businessman was responsible for the tension.

“It seems to me that they damage the relationship which Mexico has sought with the U.S.,” Mr. Peña Nieto said of Mr. Trump’s statements about Mexican immigrants in an interview with El Universal.

Mr. Trump embarked on his presidential bid last year by taking a hard line against immigration and offended many Mexicans and Hispanic Americans when he said that the country was sending drugs, criminals and rapists across the border. Two of Mexico’s former presidents condemned Mr. Trump last month, but Mr. Peña Nieto has largely avoided weighing in on the presidential election in the United States.

But as Mr. Trump edges closer to becoming the Republican nominee, Mr. Peña Nieto is expressing serious concern about his rise. He said that Mr. Trump did not understand the Mexican people and that he was capitalizing on the struggles that people are facing after the economic downturn. He also compared the solutions Mr. Trump offers to those of history’s most hated dictators.

“That’s the way Mussolini arrived and the way Hitler arrived,” Mr. Peña Nieto said in an interview with the newspaper Excelsior.

Critics of Mr. Trump have argued that he is diminishing America’s reputation in the world and that he could not be trusted to represent the country on the global stage. This year, British lawmakers debated banning Mr. Trump from the country on the grounds that he was promoting hate speech for proposing a ban on Muslim immigration.

Mr. Trump has made Mexico his favorite punching bag during campaign rallies and has threatened to tax American companies who move their operations there. When a protester interrupted a rally last month, Mr. Trump shouted back, “Are you from Mexico?”

Although he claims to admire the negotiating prowess of Mexican leaders, Mr. Trump has vowed to use unorthodox measures to compel the country to pay for the construction of the border wall, which he estimates could cost around $10 billion. After Vincente Fox, a former Mexican president, said in February that Mexico would never pay for the wall, Mr. Trump insisted that “the wall just got 10 feet taller.”

Mr. Peña Nieto promised on Monday that “there is no scenario” in which Mexico would pay for such a project.