Susan Walsh/AP
President Barack Obama salutes as soldiers carry the remains of Sgt. Dale R. Griffin of Terre Haute, Indiana in 2009.
Trump's comment came in response to a question during a Monday press briefing about why he had not yet addressed the deaths of four American soldiers in Niger, who were killed during an ambush two weeks ago.
Trump did not explain the delay, and instead attempted to defend his decision to write letters to the families by claiming that his predecessors "didn't make calls" to the relatives of fallen soldiers.
"If you look at President Obama and other presidents, most of them didn't make calls," Trump said during the 40-minute news conference with Senate Majority Leader Mitch McConnell. "A lot of them didn't make calls. I like to call when it's appropriate."
Several of Obama's former top aides responded quickly on Twitter, slamming the president's comments and calling him a liar.
"POTUS 43 & 44 and first ladies cared deeply, worked tirelessly for the serving, the fallen, and their families. Not
Former Attorney General Eric Holder tweeted a photo of himself and Obama saluting alongside several US soldiers, and wrote, "Stop the damn lying - you're the President. I went to Dover AFB with 44 and saw him comfort the families of both the fallen military & DEA."
Another longtime White House aide, Alyssa Mastromonaco, used more colorful language to express her outrage.
"That's a f---ing lie. to say president obama (or past presidents) didn't call the family members of soldiers KIA - he's a deranged animal," she wrote.
Ben Rhodes, Obama's former deputy national security adviser, brought up Trump's criticism of the parents a Muslim American soldier, Humayun Khan, who was killed in Iraq in 2004.
"This is an outrageous and disrespectful lie even by Trump standards," Rhodes tweeted, adding, "Also, Obama never attacked a Gold Star family."
Pete Souza, former White House photographer, posted an image on his popular Instagram account of Obama and first lady Michelle Obama consoling the parents of an Army sargeant awarded the Medal of Honor for his service in Afghanistan, where he was killed.
Later in Monday's press briefing, another reporter followed up on Trump's comments, asking him to clarify his charge.
Trump responded with a more equivocal statement, claiming he was repeating information provided to him by his "generals."
"I don't know if he did. I was told he didn't often, and a lot of presidents don't. They write letters," Trump said. "President Obama, I think, probably did sometimes and maybe sometimes he didn't. That's what I was told. All I can do is ask my generals."
White House press secretary Sarah Sanders responded to the criticism Monday evening, denying that Trump was making a judgment about his predecessors' treatment of the families of fallen soldiers.
"When American heroes make the ultimate sacrifice, presidents pay their respects," Sanders said. "Sometimes they call, sometimes they send a letter, other times they have the opportunity to meet family members in person. This president, like his predecessors, has done each of these. Individuals claiming former presidents, such as their bosses, called each family of the fallen, are mistaken."
Kellyanne Conway, Trump's top counselor, also denied that Trump attacked Obama, interpreting his comments as "saying that there are many different ways to reach out to these families."
"Sometimes you call, sometimes you write, sometimes you actually meet them in person," she said. "And he doesn't always make [it] public."
But on Tuesday, Trump suggested that Obama did not call John Kelly, the current White House chief of staff, after his son was killed in action in Afghanistan in 2010.
"You could ask General Kelly if he got a call from Obama," he told Fox News radio host Brian Kilmeade.