Harris took aim at Trump in a post on social media, writing that he disrespected sacred ground, all for the sake of a political stunt.
The US Army said a Trump staffer abruptly pushed aside a cemetery employee who was trying to warn his team about rules against filming in the cemetery.
The Trump campaign has disputed the cemetery’s version of events and said it received permission from the families of the fallen soldiers to film.
The incident happened, when Trump was at an event honouring 13 US military service members who were killed during the country’s withdrawal from Afghanistan three years ago.
The post marks the first time Harris, the Democratic nominee for president, has commented on the controversy.
She wrote that she has visited Arlington National Cemetery in Virginia several times during her tenure as vice-president, and she would never use the site for political gain.
At a campaign rally in Michigan on Thursday, Trump hit back at those who had criticised him over the incident.
He said he had been asked to pose for a photo at the site after the memorial by family members of the soldiers who had died.
Trump’s running mate JD Vance used the controversy to attack the Biden administration over its handling of the 2021 withdrawal from Afghanistan, saying that Ms Harris can go to hell.