"President Trump did disrespect my son and my daughter and also me and my husband," Sergeant La David Johnson's mother, Cowanda Jones-Johnson, told the Washington Post.
She said she agreed with an earlier account of the conversation given by a lawmaker who heard part of the call and accused Trump of insensitivity after he told Johnson's pregnant widow that the young soldier "knew what he was signing up for."
Frederica Wilson, a Democratic congresswoman from Florida, said she listened in to part of a group phone call between the president and the grieving family.
"I didn't hear the whole phone call, but I did hear him say, 'I'm sure he knew what he was signing up for, but it still hurts,'" she told CNN.
Trump denied making the comments, tweeting Wednesday: "Democrat Congresswoman totally fabricated what I said to the wife of a soldier who died in action (and I have proof). Sad!"
He later told reporters: "I did not say what she said," and that "I had a very nice conversation."
When asked about what "proof" he could offer, Trump said: "Let her make her statement again then you will find out."
Johnson was among four US soldiers killed October 4 in Niger, where Islamic State fighters have established a presence.
The Miami native's body was returned home Tuesday afternoon. He is survived by his wife Myeshia Johnson, who is expecting the couple's third child.
After the phone call, Myeshia "was crying, she broke down. And she said 'he didn't even know his name,'" said Wilson, referring to Trump.
Trump had faced criticism for not contacting the families of the soldiers killed in Niger right away.
At a press briefing on Monday, he said he had written them letters and would call soon, while accusing his predecessor Barack Obama of neglecting to call as many grieving families as himself.
He also suggested on a call to Fox News radio Tuesday that Obama had not made a condolence call to retired Marine general John Kelly, Trump's White House chief of staff, after his son was killed in action in Afghanistan.
The statements sparked outrage from former Obama aides, who said Trump's claims were baseless.