A White House official pushed back against comments by former vice presidential candidate Sarah Palin for implying that President Obama was somehow responsible for her veteran son's recent arrest on a domestic violence charges.

The former Alaska governor was also been criticised by the leader of a veterans' group for her comments. But Republican front-runner Donald Trump, just endorsed by Palin, has chimed in that Obama is to blame.

Press Secretary Josh Earnest indicated that the first response could be to scoff at Palin's remarks. "I can tell you that the reaction of some people is to make light of the rhetoric that we see on the campaign trail, particularly from Governor Palin, but the fact is domestic violence is not a joke," he said at his daily press briefing.

"The fact is domestic violence is not a joke. Gun violence is not a joke. Problems with addiction are not a joke and the ... sacrifices that many of our men and women in uniform make, for our safety and security, are not a joke."

Palin's eldest son, Track, who was deployed for a year in Iraq, was arrested on 18 January for allegedly punching his girlfriend in the face and having a firearm while intoxicated in the Palin family's Alaska home.

At a campaign rally the day after Palin endorsed Donald Trump for president, she appeared to attribute her son's problems to Post Traumatic Stress Syndrome that he suffered as a soldier, and seemed to blame President Obama for not respecting veterans. Track Palin, 26, served in Iraq for a year in 2008 when Republican George W. Bush was still in office.

"It's kind of the elephant in the room because my own family is going through what we're going through with my son, a combat vet," she said in a campaign speech in Oklahoma. "My son, like so many others, they come back a bit different, they come back hardened. They come back wondering if there is that respect for what their fellow soldiers and airmen and every other member of the military so sacrificially have given to the country.

"It starts from the top, the question though that comes from our own president, where they have to look at him and wonder: 'Do you know what we go through, do you know what we're trying to do to secure America and to secure the freedoms that have been bequeathed us?' "

Palin added: "I can certainly relate to the families who ... feel these ramifications of PTSD. It makes me realize more than ever it is now or never for the sake of America's finest that we have a commander-in-chief who will respect them."

The leader of a New York City veterans group told NBC News that: "it's not President Obama's fault that Sarah Palin's son has PTSD," which Paul Rieckhoff, who heads Iraq and Afghanistan Veterans of America, called a "complicated mental disease." He urged Palin to "resist the urge to politicise the issue. I hope this doesn't become a political chew toy in a political campaign," he added.

But he also noted that Track Palin may well need help for PTSD and it's a "great opportunity for Sarah Palin to sound the alarm about PTSD."

Now that "she has endorsed Mr. Trump, I would encourage her to talk with him about it," said Rieckhoff. "Mr. Trump's campaign is pretty light on specifics about what he would do for veterans."

Trump is whole-heartedly backing Palin on her comments, and said he urged her to refer to her son's arrest in her speech. Asked on CNN if it "was fair" to link the president to Track Palin's problems, Trump responded: "Oh, I think so. Look, everything starts at the top. He's the president. And I think you can certainly do that. And all you have to do is look at the Veterans Administration, and look at the bad, the horrible care our vets get."