REUTERS/Carlo Allegri
Donald Trump speaks at Wings Over the Rockies Air and Space Museum during a campaign rally in Denver, Colorado, U.S., July 29, 2016.
"Election year or not, the VFW will not tolerate anyone berating a Gold Star family member for exercising his or her right of speech or expression," VFW leader Brian Duffy said in the statement.
"There are certain sacrosanct subjects that no amount of wordsmithing can repair once crossed. Giving one's life to nation is the greatest sacrifice, followed closely by all Gold Star families, who have a right to make their voices heard."
Trump has gotten criticism from both sides of the aisle for his attacks on Khan's family. Arizona Sen. John McCain also issued a strongly worded statement on Monday condemning Trump.
"In recent days, Donald Trump disparaged a fallen soldier's parents," McCain said in the statement. "He has suggested that the likes of their son should not be allowed in the United States - to say nothing of entering its service. I cannot emphasize enough how deeply I disagree with Mr. Trump's statement. I hope Americans understand that the remarks do not represent the views of our Republican Party, its officers, or candidates."
Trump suggested Sunday morning that he could not understand why he was earning scorn for questioning the Khans after Khizr Khan slammed him Thursday night during a speech at the Democratic National Convention in Philadelphia.
"I was viciously attacked by Mr. Khan at the Democratic Convention," Trump said in a tweet. "Am I not allowed to respond?"
Khan, speaking beside his wife, Ghazala, offered a powerful rebuke of Trump on the final night of the DNC, questioning whether Trump had ever read the US Constitution or sacrificed anything for his country.
Trump hit back on Saturday, suggesting that Ghazala Khan might not have been permitted to speak at the convention because of her Muslim religion. Trump also said he had indeed sacrificed for his country, saying he created jobs.
Oliver Darcy contributed to this report.