Washington (CNN) President Donald Trump engaged in a public feud Wednesday with a Democratic congresswoman over her claim that he told the widow of a US serviceman killed in an ambush in Niger that "he knew what he signed up for, but I guess it still hurt."

In denying Florida Rep. Frederica Wilson's account of a condolence telephone call, the President created a fresh political controversy over his response to the Niger attack and his willingness to inject politics into an issue that is typically regarded as sacred by past commanders in chief.

Wilson first made the stunning claim Tuesday night, saying she was present when the call took place. Sgt. La David Johnson was among the four US soldiers killed by enemy fire in the October 4 ambush . She added on CNN's "New Day" Wednesday morning that Trump didn't know the name of the service member and that his widow "broke down" after her call with the President. Cowanda Jones-Johnson, a family member who raised Johnson, told CNN Wednesday that Wilson's account of the call between Trump and Johnson's widow, Myeshia, was "very accurate." She said she was in the car when the call happened.

Trump denied Wilson's account in both a tweet and a statement made at the White House.

"I didn't say what that congresswoman said. Didn't say it at all," Trump told reporters during a meeting on tax reform in the Cabinet Room. "She knows it. And she now is not saying it. I did not say what she said."

Trump said he had a "very nice" conversation with Johnson's widow, "who sounded like a lovely woman." Referring to Wilson, he added: "I'd like her to make the statement again because I did not say what she said."

Minutes later, Wilson responded on Twitter to Trump's remarks, saying she still stood by her account. She then told CNN affiliate WPLG that "Mr. Trump is crazy," hours after she told CNN's Alisyn Camerota that the President has a "brain disorder."

I still stand by my account of the call b/t @realDonaldTrump and Myesha Johnson. That is her name, Mr. Trump. Not "the woman" or "the wife." — Rep Frederica Wilson (@RepWilson) October 18, 2017

Trump said he has proof Wilson fabricated her claim, but neither he nor the White House immediately provided any evidence. White House press secretary Sarah Sanders said Wednesday afternoon there was no recording of the call, saying Trump was referring to several people who were present in the room at the time.

Democrat Congresswoman totally fabricated what I said to the wife of a soldier who died in action (and I have proof). Sad! — Donald J. Trump (@realDonaldTrump) October 18, 2017

Wilson on "New Day" described herself as "livid" when she heard the call on speakerphone, but when she tried to get on the phone to talk to Trump herself, a master sergeant who was present prevented her from doing so. Per military protocol, the calls from the commander in chief are solely presidential condolence conversations.

Wilson said she was ready to "curse him out" had she had the chance to get on the line. However, the Florida Democrat said she wouldn't get into the specifics of what she would have said, adding that she didn't want to "politicize" the incident.

It took Trump days to publicly discuss the attacks, and earlier this week, he falsely claimed that former President Barack Obama didn't call families of fallen service members, later suggesting reporters contact his chief of staff, John Kelly, whose son was killed in Afghanistan, to ask if Obama reached out to him.

JUST WATCHED Trump denies Wilson's claim on call to widow Replay More Videos ... MUST WATCH Trump denies Wilson's claim on call to widow 00:37

'I guess it still hurt'

Johnson's body was returned home to the Miami area late Tuesday afternoon, with the plane receiving a water cannon salute as it arrived near the gate.

The call from the President to Johnson's widow came shortly before Johnson's casket arrival, Wilson said on "CNN Tonight" Tuesday night.

"Basically, he said, 'Well, I guess he knew what he signed up for, but I guess it still hurt,' " Wilson said to CNN's Don Lemon.

"That's what he said," she added.

Asked earlier if she was sure the President said that, Wilson told CNN affiliate WPLG : "Yeah, he said that. You know ... that is something that you can say in a conversation, but you shouldn't say that to a grieving widow. Everyone knows when you go to war you could possibly not come back alive, but you don't remind a grieving widow of that. That is so insensitive. So insensitive."

A White House official said Tuesday: "The President's conversations with the families of American heroes who have made the ultimate sacrifice are private."

Wilson told WPLG that she hoped the President didn't make similar comments to the ones she heard to the other families of the soldiers killed.

"That is what stood out in everyone's heart," she said. "You don't say that. He is the President of the United States. This is a soldier who gave his life for his country. He is a hero in our minds, in our community's minds. That is an insult to the entire Miami Gardens community, to the entire District 24, to Miami-Dade County and to this nation. And I hope he didn't say that to the other three families."

JUST WATCHED Congresswoman describes Trump's call to widow Replay More Videos ... MUST WATCH Congresswoman describes Trump's call to widow 05:22

Evokes Khan family feud

12 days after they were killed. Trump first publicly addressed the soldiers' deaths in a Rose Garden news conference12 days after they were killed.

"I felt very, very badly about that," Trump said Monday. "I always feel badly. It is the toughest calls I have to make are the calls where this happens, soldiers are killed."

He then claimed that other commanders in chief hadn't reached out to families of Americans killed in action, saying he'd been told as much by the generals who serve in his administration. On Tuesday, Trump bragged about calling loved ones from all those killed in action during his presidency.

"I really speak for myself. I am not speaking for other people. I don't know what (George W.) Bush did. I don't know what Obama did," Trump said. "I believe his policy was somewhat different than my policy. I can tell you, my policy is I have called every one of them."

Trump told reporters to ask Kelly if he received a call from Obama when his son was killed while serving in Afghanistan in 2010.

"As far as other presidents, I don't know, you could ask Gen. Kelly, did he get a call from Obama? I don't know what Obama's policy was," Trump said during a Fox News Radio interview Tuesday. CNN asked the White House to talk to Kelly about this issue, but they declined to make him available. Kelly also has not responded to a direct request from comment from CNN.

Following Wednesday's back-and-forth between Trump and Wilson, Karen Meredith, who lost her son, 1st Lt. Ken Ballard, in Iraq, called the President's remarks "disgraceful" and "unbecoming."

JUST WATCHED Gold Star dad: Trump's words misconstrued Replay More Videos ... MUST WATCH Gold Star dad: Trump's words misconstrued 01:29

"Mr. Trump, stop. Please, just stop," Meredith, the Gold Star and Military Families coordinator for VoteVets, said in a statement. "This is not about you, it is about them. It is about all of us who lost our loved ones in war. For once in your life, please stop making everything about you. For once in your life, at least pretend to know what empathy is. For once in your life, at least try to care about other people and their feelings."

Outrage over Trump's alleged comments to Johnson's widow evoke a similar controversy to his public feud with the family of another fallen American soldier.

During last year's campaign, Khizr and Ghazala Kahn, the parents of Capt. Humayun Khan, who was a Muslim American, criticized him from the stage of the Democratic National Convention . Trump responded by saying the family "viciously attacked" him.

Before Trump's alleged comments on Johnson surfaced, the Khans issued a statement Tuesday accusing Trump of a "lack of empathy" and of "selfish and divisive" conduct that undermined the dignity of the presidency.

"One more time, he has shown us that he is undeserving of the leadership of our great nation," the family's statement said.

CORRECTION: This story has been updated to reflect that Wilson was the principal of Johnson's father.