WASHINGTON (Reuters) - Aides to former U.S. President Barack Obama fired back on Tuesday as criticism mounted over President Donald Trump’s claim that past U.S. presidents did not contact family members of soldiers who died in combat during their time in the White House.     Trump offered no evidence to back up his claim on Monday, which was immediately pointed out to be false. His remarks came amid questions at a press conference over Trump not having responded yet to the deaths of four U.S. soldiers in an Oct. 4 ambush in Niger. Asked why he had not acknowledged the soldiers’ deaths, Trump said he would send letters to their families later on Monday and would call them “at some point during the period of time.” Obama’s former White House spokesman Josh Earnest said on Tuesday that Obama 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 phonecalls and letters. Trump, a Republican who as president serves as commander-in-chief of the U.S. military, then appeared to criticize his predecessors handling of the issue of American soldiers’ deaths.  “The traditional way, if you look at President Obama and other presidents, most of them didn’t make calls. A lot of them didn’t make calls,” Trump said. Pressed on his claim, particularly about Obama, Trump retreated.     “I don’t know if he did. No,” Trump said. “I was told that he didn’t often, and a lot of presidents don’t. They write letters ... I do a combination of both.” “President Obama, I think, probably did sometimes, and maybe sometimes he didn’t. I don’t know. That’s what I was told,” Trump added. “Other presidents did not call, they’d write letters. And some presidents didn’t do anything.”  Obama’s former aides were quick to lash back.  “Stop the damn lying - you’re the President,” Eric Holder, Obama’s former attorney general, said in a post on Twitter.  Alyssa Mastromonaco, Obama’s former deputy chief of staff, also called it a lie. Earnest, now an MSNBC commentator, told the network that past Republican and Democratic presidents had recognized their duty to honor soldiers’ sacrifices and not highlight their own actions. “Unfortunately, President Trump seems incapable of actually doing that,” Earnest said. A spokesperson for former President George W. Bush said he had called, written and visited the families of fallen soldiers. Representatives of former Presidents Bill Clinton, George H. W. Bush and Jimmy Carter either did not immediately respond to a request for comment or did not have an immediate reaction.  An aide to Clinton told ABC News that he did call the families of fallen soldiers. 