Wilson, who overheard the call on speakerphone, reported that Trump said Johnson "knew what he signed up for ... but when it happens it hurts anyway".
And while Trump got on Twitter on Wednesday and accused Wilson of fabricating what he said, at no point did Kelly refute her version of the events. La David Johnson, was disrespected by Trump in a phone conversation with his widow, according to the aunt who raised him.
"I feel very sorry for him because he feels such a need to lie on me and I'm not even his enemy", Wilson told the newspaper.
Sarah Sanders, the White House press secretary, said Kelly "absolutely" stands by his slam.
Wilson said Kelly's comment was a fabrication, that she wasn't even elected to Congress when the funding for the building was approved.
Trump on Wednesday accused Representative Frederica Wilson of lying about what the president told a widow of one of four USA soldiers killed in Niger earlier this month-and he said he can prove it. He knew what he was getting into by joining that one percent.
"I was stunned that she had done that", he said on Thursday.
"If you want to go after General Kelly, that's up to you", Sanders said.
A Johnson family member, who also heard the conversation, backed up Wilson's account. Kelly himself said during the briefing that he had advised Trump not to make the calls, saying that neither President Barack Obama nor President George W. Bush called families in every case, and Trump should have heeded that advice. In response, Kelly told him what General Joseph Dunford, now chairman of the Joint Chiefs of Staff, told him when Robert Kelly was killed.
The uproar over Trump and how presidents should or shouldn't try to console families of the fallen has rattled the White House and overshadowed the rest of Trump's agenda in recent days. During her speech, Wilson said, "It is a miracle, to say the least, but it speaks to the respect that our Congress has for the Federal Bureau of Investigation".
Islamic militants on motorcycles brought rocket-propelled grenades and heavy machine guns, killing the four and wounding others after shattering the windows of unarmored USA trucks.
"I know more about ISIS than the generals do, believe me", he said. Those calls, he said as he fought back tears, were the most important.
Kelly personally absolved Trump of blame in his call to the family of Sgt.
Brianna Keilar was struck by Huckabee Sanders' "absurd statement" about the media continuing to cover this, while former retired Rear Admiral and State Department spokesman John Kirby agreed that of course Kelly "should be questioned" and scrutinized by the press.
He also described how he and his wife learned of their own son's death. So did other people in the White House.