"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 is making her first appearance with First Lady Michelle Obama.
The two shared a stage at Winston-Salem in North Carolina.
Introducing Mrs Obama, the former first lady said her voice was needed in this election "more than ever".
Mrs Clinton referred to Mr Trump's ongoing feud with the Khans and accused him of "rubbing salt into the wounds of a grieving family".
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."
In other campaign developments:
Former Illinois Representative Joe Walsh tweeted: "On November 8th, I'm voting for Trump. On November 9th, if Trump loses, I'm grabbing my musket. You in?"
He later said he was speaking metaphorically about "acts of civil disobedience".
Mrs Clinton's campaign is dealing with more questions arising from hacked emails published by Wikileaks.
The Trump campaign has seized on the latest dump to suggest the line between Bill Clinton's personal income and the donations for the Clinton Foundation has been blurred.
Doug Band, a top aide to Mr Clinton, said in an email that he had solicited donations to the foundation and also generated personal income for him through gifts and paid speeches.
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Suleiman Al-Sadi, from Bristol, said members of staff at a store in the city whistled and laughed at him while he was shopping for a sofa last Tuesday.
He said he was "shocked and horrified" when they made jokes about his "camp" appearance.
DFS said an investigation was under way and several staff had been suspended.
Mr Al-Sadi said "five sales guys" looked at him and started laughing when he walked into the shop at Cribbs Causeway.
He said one of them joked they "should probably take him to look around the beds".
"I was shocked, confused, horrified. A couple of them started whistling. I felt like I'd stepped back into the 1970s.
"They were trying to taunt me. It was making fun and jokes of my appearance. They didn't take me seriously."
Mr Al-Sadi complained to DFS. The company said it was "disappointed" to hear of the allegations and was "taking it extremely seriously".
A spokesman said: "We have apologised to the customer for any unintentional distress caused and remain in regular dialogue with him as we look into the issue further.
"Following the complaint, a formal investigation is under way and several employees have been suspended pending completion of the investigation.
"Should anyone be found to have breached our standards, further disciplinary action will be taken."
Republican Donald Trump has been criticised by the family of a dead US soldier after saying as president he would have kept him alive.
[NEXT_CONCEPT]
A number of employees at a DFS furniture store have been suspended over allegations they made fun at the appearance of a customer.