"A lot of them didn't make calls", Trump said on Monday, later adding that he didn't know whether President Obama in particular called fallen soldiers' families.
The president, engulfed in controversy over the appropriate way for presidents to show compassion for killed soldiers, strongly disputed that account.
But Johnson's mother backed Wilson's account. "I was in the auto and I heard the full conversation".
Trump denied that account in a tweet and said he had "proof".
"Didn't sai (say) it at all", Trump told reporters at the White House hours later, insisting that he had a "very nice" conversation with the widow.
Ms Wilson did not back down from her account, suggesting Mr Trump "never wants to take ownership" of a mistake. "That's what the President tried to say to the four families the other day".
"Well, I guess he knew what he signed up for, but I guess it still hurts", Wilson recounted Trump's words during an interview with CNN. She said she was in the vehicle when the call happened.
"Disappointed that he at least didn't call and thank me for my son and our ultimate sacrifice", said Mark Hunter, whose 23-year-old son Army Sergeant Jonathon Hunter was killed in Afghanistan in August of this year. "She said he didn't even remember his name".
Trump asserted that former President Barack Obama didn't call families of fallen service members, a claim that aides of the former administration slammed as "an outrageous and disrespectful lie".
What is different is that Mr Trump alone has picked a political fight over who has done better to honour the war dead and their families. "President Trump did disrespect my son and my daughter and also me and my husband", Cowanda Jones-Joshnson told The Washington Post.
Democratic senator Tammy Duckworth, an Iraq veteran who lost both legs when her helicopter was attacked, said: "I just wish that this commander in chief would stop using Gold Star families as pawns in whatever sick game he's trying to play here". A White House official claimed to NBC News, on background, that Mr Kelly never received a call from Mr Obama after his son's death.
Kelly said he advised Trump not to make the calls because it was so hard to deliver such a tragic message.
He equivocated on Tuesday as the record made plain that his characterisation was false.
Kelly did say that he believed phone calls and even letters from USA presidents could not "lighten the burden on these families" and said he advised Trump against the phone calls. But he said his own practice was to call all families of the war dead.