Other people accused Trump of making blasphemous lies on a national stage about Obama.
CNN asked the White House to talk to Kelly about this issue, but they declined to make him available.
"The traditional way, if you look at President Obama and other presidents ― majority didn't make calls".
Trump was asked on Monday why he had not yet commented on the deaths of four US soldiers who were ambushed during a mission in Niger on October 4. "Instead of saying 'No, I haven't called them yet and I'm going to call them, ' basically did the reprehensible disgusting, soulless, callous thing of lying that these past presidents hadn't done it".
Mr Trump alluded to General John Kelly's son while defending his claim that his predecessor neglected to call the loved ones of fallen soldiers.More news: Three dead as Storm Ophelia batters Ireland
He also claimed, without merit, that his predecessors hadn't written or called the families of slain American troops during their tenures, though the tradition of presidents reaching out after USA servicemen are killed in action is long-established.
Not only did Obama call to pay his respects to the fallen when he was president, but he did it in person on numberous occasions.
But I do know the memory of 1st Lt. Robert Michael Kelly doesn't deserve to be treated as a partisan prop by a draft-dodging amateur whose profound insecurities overrides any sense of moral judgment he has left.
During the 2016 Democratic convention, Khizr Khan, father of Muslim U.S. Army Captain Humayun Khan, who died in Iraq while trying to protect his men during an attack, denounced Trump's Islamophobic stances, and asked whether Trump had "even read the United States Constitution". "It is the toughest calls I have to make are the calls where this happens, soldiers are killed".
Furious over the remarks, many have been unloading on Trump.More news: Micromax Launches Bharat-1 4G Feature Phone With BSNL At Rs 2200
Alyssa Mastromonaco, a former senior aide to Obama, tweeted that it was "a (expletive) lie" and called Trump a "deranged animal".
A spokesperson for former President George W. Bush said he had called, written and visited the families of fallen soldiers.
Barack Obama, during his term in office, wrote letters and made calls to families of killed Americans, according to former administration officials.
The breakfast, hosted by the Obamas, was scheduled six months after the death of General Kelly's son. "I was told [Obama] didn't often, and a lot of presidents don't".
He said President Bush also called or met "hundreds, if not thousands" of family members of the war dead. I don't know what Bush did, I don't know what Obama did. I don't know. That's what I was told.More news: US Supreme Court agrees to resolve Microsoft foreign email battle
Trump was called out on the claim a few minutes later by NBC News White House Correspondent Peter Alexander, and he backtracked on the comments.