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Mike Pence said he and Trump believe Khan "is an American hero and his family, like all Gold Star families, should be cherished by every American."
"Captain Khan gave his life to defend our country in the global war on terror," the Indiana governor, who is Trump's running mate, wrote. "Due to the disastrous decisions of Barack Obama and Hillary Clinton, a once stable Middle East has now been overrun by ISIS. This must not stand."
"By suspending immigration from countries that have been compromised by terrorism, rebuilding our military, defeating ISIS at its source and projecting strength on the global stage, we will reduce the likelihood that other American families will face the enduring heartbreak of the Khan family," he said. "Donald Trump will support our military and their families and we will defeat the enemies of our freedom."
Trump suggested Sunday morning that he could not understand why he was earning scorn for questioning the pair of Gold Star parents who slammed him during a speech before the Democratic National Convention in Philadelphia on Thursday.
"I was viciously attacked by Mr. Khan at the Democratic Convention," the Republican nominee for president asked in a tweet. "Am I not allowed to respond?"
Khizr and wife Ghazala Khan, the parents of Humayun, offered a powerful rebuke to Trump on the final night of the DNC.
In an eight-minute speech, delivered by Khizr, the family questioned whether the New York businessman had ever read the US Constitution or sacrificed anything for his country.
Trump hit back on Saturday, suggesting Ghazala was not permitted to speak because of her Muslim religion. The billionaire further argued that he had indeed sacrificed for his country, saying he created jobs.
Trump's remarks were widely condemned and the billionaire eventually began walking them back. In a Saturday night statement, he called the Khan's son a "hero to our country" and tried to shift the issue to "the real problem" which he argued was "the radical Islamic terrorists who killed him."
Khizr Khan said Sunday that Trump's questions about his wife represent the "height of ignorance."
Ghazala Khan also wrote an op-ed in The Washington Post saying she didn't speak at the DNC because she finds it too painful to think about her son.
"Without saying a thing, all the world, all America, felt my pain," she wrote.
Oliver Darcy contributed to this report.