By Dan Merica, CNN

(CNN) -- President Donald Trump, in defense of his claim that President Barack Obama didn't call the loved ones of fallen soldiers, floated the idea Tuesday that reporters ask his chief of staff, retired Gen. John Kelly, whether Obama called him after his son died in Afghanistan.

The comment came during an interview on Fox News Radio.

"As far as other presidents, I don't know, you could ask Gen. Kelly, did he get a call from Obama? I don't know what Obama's policy was," Trump said.

Kelly's son Robert died when he stepped on a landmine in Afghanistan in 2010. Kelly, a retired four-star Marine general, was a lieutenant general at the time.

Multiple White House officials have told CNN that Obama did not call Kelly when his son was killed.

CNN asked the White House to talk to Kelly about this issue, but they declined to make him available. Kelly also has not responded to a direct request from comment from CNN.

"I write letters and I also call," Trump said of himself. "I have called, I believe everybody, but I will use the word virtually everybody."

In the first year of Obama's term, 466 American troops died in Iraq and Afghanistan, compared to 25 this year. A spokesman for Obama declined a CNN request for comment about Trump's remarks.

Kelly and his wife, Karen Hernest Kelly, were invited to attend a 2011 Memorial Day breakfast for Gold Star families, those men and women whose children were killed in action, according to an aide, speaking on background.

White House visitor logs from that day show that Kelly and his wife were cleared to attend the event. A person familiar with the breakfast says that General and Mrs. Kelly were scheduled to sit at Michelle Obama's table, but CNN could not determine if they were present.

On Tuesday, Trump bragged about calling loved ones from all those killed in action during his presidency.

"I really speak for myself. I am not speaking for other people. I don't know what (George W.) Bush did. I don't know what Obama did," Trump said. "I believe his policy was somewhat different than my policy. I can tell you, my policy is I have called every one of them."

Trump said on Monday he'd written letters to the families of the slain American soldiers, and planned to phone them in the near future.

Kelly, according to media reports, has tried to keep his son's death private.

The Washington Post, in a 2011 profile of Kelly, reported that the general asked a Marine Corps officer not to mention his son's death when he was introduced at a St. Louis event days after his son was killed.

Clarification: An earlier version said the Kellys attended the 2011 Memorial Day breakfast. White House records only show they were cleared in to attend.