The president was responding to Congresswoman Frederica Wilson's claim he had made the "insensitive comments" moments before the funeral of Lance Sergeant David Johnson. He was one of four Green Berets killed when their patrol was ambushed by Islamist militants in Niger.

He claimed not only that the Florida congresswoman who reported the phone call was wrong, but that she had intentionally lied. He has "proof" of that fact, he said.

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"Democrat Congresswoman totally fabricated what I said to the wife of a soldier who died in action (and I have proof). Sad!" he wrote on Twitter.

Mr Trump didn't say what proof he had collected. The White House had originally told the press that the phone calls between the president and families would be kept private.

Ms Wilson had told CNN that she overheard the phone call, and repeated her claim about Mr Trump's offensive comment.

"Basically he said, 'Well I guess he knew what he signed up for, but I guess it still hurts’,” she claimed. "I heard what he said because the phone was on speaker."

When asked by Miami station WPLG if she indeed heard Trump say that she answered: "Yeah, he said that. To me, that is something that you can say in a conversation, but you shouldn't say that to a grieving widow."

She added: "That's so insensitive."

Later, reacting to Mr Trump's tweet, Ms Wilson said that the president was a "sick man". "I don't know what kind of proof he could be talking about – I'm not the only person that was in the car, and I have proof too" she said.

"This man is a sick man, he's cold-hearted and he feels no pity or sympathy for anyone," she told CNN.