"The traditional way if you look at President Obama and the other presidents, majority didn't make calls, a lot of them didn't make calls", he said.
Trump later walked back his comments after pressure from a reporter.
Trump himself failed to support his own assertion later in the press conference, when he was asked how he could claim to know whether Obama did or did not call grieving military families.
"This is an outrageous and disrespectful lie even by Trump standards", said Ben Rhodes, Mr Obama's foreign policy adviser.
"I really speak for myself".
He added, "I'm not speaking for other people".
"I don't know. That's what I was told".
"It's been the furthest thing from my mind and the minds of my family", said Will Wright, the brother of Staff Sgt. Dustin Wright, adding he bore no ill-will toward Trump.
A White House official later told NBC News that Obama did not call Kelly when his son was killed in 2010 - but it wasn't clear if the president had written to him or called or written the younger Kelly's widow.
Donald Trump has brought up General John Kelly's dead son, Robert, to prove a point.
"President Obama, I think probably did sometimes, and maybe sometimes he didn't".
North Korean Slave Labor Used to Process Fish Sold in US Stores
Some of those companies have already cut off those parts of their supply chains, others said they are investigating the matter. Information for this article was contributed by Martha Mendoza, Leonardo Haberkorn, Han Guan Ng, Fu Ting, Kelvin K.
Generally, former Obama aides said, the president wrote letters or made base visits in which he met with families. With an expletive, she called his statement in the Rose Garden a lie.
Eric Holder, President Obama's former attorney-general, called on Mr Trump to tell the truth.
Here is one of those occasions, shared by AM Joy contributor Scott Dworkin, when the former president flew to DE at midnight in 2009 to meet with family members and pay his respects to 18 soldiers killed in Afghanistan.
"I also photographed him meeting with hundreds of wounded soldiers, and family members of those killed in action", he wrote.
President Donald Trump falsely asserted on Monday that his predecessor, Barack Obama, and other presidents did not contact the families of American troops killed in duty, drawing a swift, angry rebuke from several of Obama's former aides.
The path to Walter Reed and other military hospitals, as well as to the Dover, Delaware, Air Force Base where the remains of fallen soldiers are often brought, is a familiar one to Mr Obama, George W. Bush and others. "Not politics. Sacred Trust".
White House press secretary Sarah Huckabee Sanders told TPM in an email that "The President wasn't criticizing predecessors, but stating a fact".
Trump said that over the weekend letters had been drafted for the families and would be "going out either today or tomorrow".
She said anyone claiming a former president had called every family was "mistaken".
Trump, a Republican who as president serves as commander-in-chief of the US military, then appeared to criticize his predecessors handling of the issue of American soldiers' deaths.
That reference was to the public feud Trump began with the parents of a Muslim-American soldier, Humayun Khan, who was killed in Iraq in 2004.
The former POW and Arizona Republican called the USA "the last best hope on earth" while giving an acceptance speech for the National Constitution Centre's Liberty Medal, reports The New York Post, citing a Politico report.