He said it was possible that Mr Obama "did sometimes" but "other presidents did not call".
President Obama breaks record for pardons during his tenure in the White House.
"The traditional way, if you look at President Obama and other presidents, majority didn't make calls, a lot of them didn't make calls", Trump said when asked about the four Green Berets killed earlier this month in Niger.
"I think I've called every family of someone who's died", Trump said during an interview. "I don't know what Obama's policy was", Mr Trump said on Fox News Radio.
Former President Obama aides did not take Trump's claim lightly. "Obama and other presidents" most certainly made calls.
Sharon Belkofer, a Gold Star mother whose son died in 2010 in Afghanistan, told the Democratic National Convention in 2016 that she met Obama at Ft. "He saw up-close just how -& how much - Obama cared for the fallen's families", Price tweeted Tuesday. "But when we got on Marine One to fly back to the White House, the president was looking out the window, and then he looked at me and he said, 'That mama sure was mad at me.' And then he looked out the window and he said, 'And I don't blame her a bit.' And a tear rolled down his cheek, but he didn't wipe it away, and then we flew back to the White House".
Trump made his remark when asked about how he would respond to an ambush attack from ISIS related militants in Niger earlier this month that left four USA servicemembers dead.
"I don't know. That's what I was told". "I like, when I can, the combination of a call and also a letter".
Former White House defense secretary and chief of staff Leon Panetta said that Obama made calls to families in 2011 after 30 soldiers died in a helicopter explosion in Afghanistan - Obama and Panetta flew to the DE air force base to meet with families as the soldiers' remains were delivered home, the Post reports.
"Unfortunately, President Trump seems incapable of actually doing that", Earnest said. "Sometimes they call, sometimes they send a letter, other times they have the opportunity to meet family members in person". "I don't know. That's what I was told", Trump added.
George W. Bush also wrote letters to families of troops killed in the wars in Iraq and Afghanistan, which began during his tenure.
Mr Obama's former White House spokesman Josh Earnest said that his boss would repeatedly "show his enormous respect. for those who had paid the ultimate sacrifice for our country" through various visits and meetings as well as phone calls and letters.
Trump told reporters he planned to call the parents and families of those who were killed. "All I can do is ask my generals".
Gen Kelly has yet to comment on the president's latest remarks.