"Had I been president, Captain Khan would be alive today. We wouldn't have been in this horrible, horrible mistake, the war in Iraq," he said.
The soldier's father, Khizr Khan, said it was a "cruel" remark.
He is campaigning for Hillary Clinton, who makes her first joint appearance with First Lady Michelle Obama later.
Mr Khan's son Humayun was killed by a car bomb in 2004 in Iraq at the age of 27.
Their grief became part of the presidential campaign in July when Khizr Khan made an emotional speech at the Democratic Convention attacking Mr Trump for anti-Muslim rhetoric, as his wife stood next to him.
The Republican candidate's reaction, in which he implied the mother was not allowed to speak up, attracted strong condemnation from within his own party.
Speaking to ABC News in an interview aired on Thursday, Mr Trump repeated his insistence that their son would be alive, but added he believed the soldier was a "great hero".
In response, Mr Khan said: "This is the most cruel thing you can say to grieving parents, that if I was there this would not have happened."