Phillip Carter, a professor who is a US Army veteran, responded to the Atlantic article on Twitter, writing that a president who asked what Trump was said to have asked in a place like Arlington was not suited to be commander in chief.
Griffin also said one of her sources said, "It was a character flaw of the President". "French President Macron had said something that made him mad, he questioned why he had to go to two cemeteries".
Domenech is the husband of Meghan McCain and son-in-law of the late Arizona Sen.
"I'm confident I have better sources within this White House than @JeffreyGoldberg, and I expect that upon investigation his anonymously sourced story will live up to the quality we can expect from The Atlantic under his leadership", Domenech tweeted Thursday evening.
The Atlantic's reporting was based on anonymous sources but a "senior Defense Department official with first-hand knowledge of events" and a "senior U.S. Marine Corps officer who was told about Trump's comments" confirmed the cemetery comments to AP.
What is Trump reported to have said?
The President, now, wants that journalist fired for reporting "fake news".
The US president and his allies have dismissed the report in The Atlantic as false.
The number of former Republican lawmakers and officials endorsing Democratic presidential nominee Joe Biden continues to grow as a new group representing nearly 100 prominent Republicans including several former governors endorsed the former vice president on Thursday.
AstraZeneca Launches 30000-Patient Phase III US Trial of COVID-19 Vaccine
Developed in partnership with Oxford University , AZD1222 employs the husk of an inactivated virus to deliver genetic material. AZD1222 is seen as one of the leading hopes among dozens of coronavirus vaccine candidates in development around the world.
"I've just never been as disappointed, in my whole career, with a leader that I've worked with, president of otherwise", said Mr Biden.
"Mr. President, if you don't respect our troops, you can't lead them", he tweeted.
Trump said: "He lost [the 2008 election], so I never liked him as much after that because I don't like losers".
Thursday night, Trump tried to recast the narrative of his criticism of McCain by boasting that he approved the plans for McCain's funeral in 2018.
Where do Trump and the USA military stand?
Khizr Khan, the father of a United States soldier killed in Iraq who criticised Mr Trump during the 2016 Democratic convention, joined Ms Duckworth on the call.
But there have been previous spats and controversies.
Media captionTrump and the USA military: Friends or foe? People close to the retired general said that he first thought the president was awkwardly commenting on the selflessness of America's service members, particularly those who laid down their lives, but later came to believe that Trump did not understand sacrificing for others. He received five deferments from a military draft during the Vietnam War - four for academic reasons and one for bone spurs, a calcium build-up in the heels.