"I said, 'Me and my wife would rather our son died in trench warfare,' " Baldridge said. "I feel like he got murdered over there."
Trump's offer of $25,000 adds a dimension to his relationships with Gold Star families, and the disclosure follows questions about how often the president has called or written to the parents or spouses of those killed.
The Washington Post contacted the White House about Baldridge's account on Wednesday morning. Officials declined to discuss the events in detail.
But in a statement Wednesday afternoon, White House spokeswoman Lindsay Walters said: "The check has been sent. It's disgusting that the media is taking something that should be recognized as a generous and sincere gesture, made privately by the President, and using it to advance the media's biased agenda."
It took 18 months for President Barack Obama to fulfill a similar promise made to the family of Kayla Mueller, who was killed in 2015 while she was held captive by the Islamic State in Syria. Obama's undisclosed sum, for a charity set up in Mueller's name, arrived only after a report by ABC News called attention to what the president later described as an oversight.
Trump said this week that he has "called every family of somebody that's died, and it's the hardest call to make." At least 20 Americans have been killed in action since he became commander in chief in January. The Post interviewed the families of 13. About half had received phone calls, they said. The others said they had not heard from the president.
In his call with Trump, Baldridge, a construction worker, expressed frustration with the military's survivor benefits program. Because his ex-wife was listed as their son's beneficiary, she was expected to receive the Pentagon's $100,000 death gratuity — even though "I can barely rub two nickels together," he told Trump.
The president's response shocked him.
"He said, 'I'm going to write you a check out of my personal account for $25,000,' and I was just floored," Baldridge said. "I could not believe he was saying that, and I wish I had it recorded because the man did say this. He said, 'No other president has ever done something like this,' but he said, 'I'm going to do it.' "
The president has been on the defensive since details emerged of his phone call Tuesday with the widow of Sgt. La David T. Johnson, who was killed Oct. 4 along with three other U.S. soldiers in Niger. After not addressing the incident for 12 days, Trump on Monday falsely claimed that previous presidents never or rarely called the families of fallen service members. In fact, they did so regularly.
White House officials circulated a statement of sympathy for the soldiers killed in Niger after the attack, but it was never released, Politico reported Wednesday. It is not clear why the statement was never released, but it was prepared when the Pentagon had said only that three soldiers were killed and before officials disclosed that a fourth soldier, Johnson, also was killed. His body was recovered Oct. 6, two days after the attack.
Rep. Frederica S. Wilson (D-Fla.) said Trump called Johnson's widow, Myeshia Johnson, on Tuesday and said her husband "knew what he was signing up for, but I guess it hurts anyway." Wilson was riding in a limousine with the widow and said she heard the conversation on speakerphone.
Attempts to reach Myeshia Johnson on Wednesday were unsuccessful.
Trump denied the allegation Wednesday, saying in a tweet that Wilson had "totally fabricated" what happened and that he had "proof." But the soldier's childhood guardian, Cowanda Jones-Johnson, told The Post that she also was in the car when Trump called, and said that "President Trump did disrespect my son and my daughter and also me and my husband."
Trump later expanded his denial, saying that he did not say what Wilson alleged and that "she knows it."
He added: "I had a very nice conversation with the woman, with the wife who was — sounded like a lovely woman. Did not say what the congresswoman said, and most people aren't too surprised to hear that."
White House press secretary Sarah Huckabee Sanders defended the president, saying in a news briefing that Trump was "completely respectful" during the call. Several White House officials, including Chief of Staff John F. Kelly, were in the room at the time, she said.
In all, seven Gold Star families contacted by The Post said they have had phone conversations with Trump. Most said they appreciated the gesture. Four other families said they have not received a call and were upset. One said Trump had not called but that they knew the late soldier would not want his death politicized. An additional family said it had corresponded with the White House but declined to elaborate.
The Associated Press reached one other family, that of Army Spec. Etienne Murphy, 22. His mother said she received neither a call nor a letter from the president.
Baldridge said that after the president made his $25,000 offer, he joked with Trump that he would bail him out if he got arrested for helping. The White House has done nothing else other than send a condolence letter from Trump, the father said.
"I opened it up and read it, and I was hoping to see a check in there, to be honest," the father said. "I know it was kind of far-fetched thinking. But I was like, 'Damn, no check.' Just a letter saying 'I'm sorry.' "
The experiences of other Gold Star families were more typical.
The family of Sgt. Cameron H. Thomas, a 23-year-old Army Ranger killed April 27 in a raid on the Islamic State in Afghanistan, met with Vice President Pence at Dover Air Force Base in Delaware as the soldier's casket arrived from overseas. They had a 20-minute call with Trump about two weeks later, said Thomas's father, Andre.
"He gave his condolences and made some comments how different his paperwork was when it went across his desk," the father said in a phone interview. "Said most of the paperwork he sees in these types of death says, 'He's respected by his peers.' He said Cameron's stuck out because it said he was respected and loved by his peers."
Thomas said he spoke at length about his son's love for the Army and his determination to become a Ranger, a distinction he earned at age 19. About midway through the phone call, Thomas said he told Trump that he had voted for him, and "that got him on another tangent" that extended the conversation for about 10 minutes."
The president then spoke about his work in office and "the strides that he's made in the short time he'd been president," Thomas said.
Thomas said the family was touched by the phone call. The father of a Mormon family with 12 children, seven of them adopted, Thomas said he was concerned about the attention that his son's death could bring. But talking to the president helped him put things in perspective and realize that his son "belonged to the country."
"Politics is politics, and maybe some people wouldn't care to hear from him," he said. "But putting politics aside, it does mean a lot to a family, their child."
William J. Lee, 40, said his entire family spoke by phone with Trump after his brother, Army 1st Lt. Weston Lee, 25, was killed in Mosul, Iraq, on April 29.
"He was very cordial and very nice," Lee said, of the call, which he said lasted about five or six minutes.
Lee said the president spoke to them about "how impressive my brother was, how he had read the reports, reading everything about Weston, and he could tell how amazing he was. And talking to us, he could tell how strong we were and how strong he must have been. We were all pretty devastated.
"It meant something, the leader of our nation calling us and showing the honor and respect to my brother that I feel my brother earned," Lee said, his voice cracking.
Quinn Butler, whose 27-year-old brother, Aaron, was killed in August by an explosion in Afghanistan, said that their parents received numerous letters from generals and other leaders, but no call or letter from Trump.
Staff Sgt. Aaron Butler, a Special Forces soldier, was very supportive of Trump and appreciative for what he has done for the military, his brother said. Quinn Butler said his brother believed that Trump helped initiate some changes that have enabled commanders to make more progress against the militants in Afghanistan.
Butler said that he was surprised that his parents did not receive a call from Trump, considering his brother was a "very elite soldier, a soldier who had given everything." But he said that the soldier would not want his death politicized.
"I think that Aaron would be very upset if anything was manipulated to show that he didn't support Trump and that he wasn't appreciative of the things that he did do, because he was," the brother said.
Euvince Brooks's son, Sgt. Roshain E. Brooks, 30, was killed Aug. 13 in Iraq. He has not heard from the White House. The president's claim this week that he had called every military family to lose a son or daughter only upset the Brooks family more.
Brooks said that after watching the news on Tuesday night he wanted to set up a Twitter account to try to get the president's attention.
"I said to my daughter, 'Can you teach me to tweet, so I can tweet at the president and tell him he's a liar?'" he said. "You know when you hear people lying, and you want to fight? That's the way I feel last night. He's a damn liar."
Julie Tate, Anne Gearan and Kristine Phillips contributed to this report.