The incident has mushroomed into an uncharacteristically public dispute between the military and a former US commander in chief, with Trump lashing out and accusing President Joe Biden and Vice President Kamala Harris of having "killed" American soldiers through "gross incompetence" in Afghanistan.

Trump went to Arlington National Cemetery just outside Washington with family members of some of the 13 service members killed in a 2021 bombing during the last hours of the US withdrawal from Afghanistan.

His campaign posted photos from the visit, including one showing him giving a thumbs-up gesture while standing with relatives at the grave of one of the US Marines killed.

The Army said an Arlington employee was "abruptly pushed aside" when she sought to ensure a law prohibiting political activity on cemetery grounds was followed.

"This incident was unfortunate, and it is also unfortunate that the (Arlington National Cemetery) employee and her professionalism has been unfairly attacked," an Army spokesperson said in a statement.

Going on the offensive, Trump's campaign co-manager Chris LaCivita has described the employee as a "despicable individual," while campaign spokesman Steven Cheung said she was "clearly suffering from a mental health episode."

Doubling down, LaCivita later reposted video of Trump's presence at Arlington and said he hoped it would "trigger the hacks" at the US Army secretary's office.

Trump has made criticism of Biden's handling of the retreat from Afghanistan a key note of his campaign ahead of November's election.

The US withdrawal was made as part of a peace deal signed by the Trump administration with the Taliban.

At a Thursday rally in Michigan, Trump defended his gravesite visit and savaged Biden and Harris, his 2024 White House rival, over Afghanistan.

"They asked me to go yesterday to Arlington and I did," Trump said of the families, adding that "bad people" accused him of inappropriate political activity.

"Joe Biden killed their children, by incompetence... Kamala killed their children -- just as though they had a gun in their hand -- by gross incompetence," Trump told supporters.

"Not one general or incompetent bureaucrat was fired," over the deadly pullout, he added. "And then they accuse me of having a picture taken at the tombstone with the family."

Uproar over the incident at Arlington on Monday is the latest controversy in Trump's troubled relationship with the military.

While often touting his support for the armed forces, he privately mocked the war dead while he was president and did not want to be seen near military amputees, according to his former chief of staff.