Having criticised Obama’s foreign policy in a high-profile interview published in The Atlantic, Hillary Clinton appeared to have sought to soothe relations between the two camps on Tuesday.

“While they’ve had honest differences on some issues, including aspects of the wicked challenge Syria presents, she has explained those differences in her book and at many points since then,” a Clinton spokesman said in a statement. “Some are now choosing to hype those differences but they do not eclipse their broad agreement on most issues.”

Mrs Clinton was Obama’s secretary of state during his first term and is widely accepted to be in the midst of an as-yet unofficial run for the White House in 2016.

She said in the Atlantic interview “great nations need organising principles, and ‘don’t do stupid stuff’ is not an organising principle”. The comment was aimed directly at Obama who has recently been quietly briefing reporters off-record that the key to understanding his reticence to engage in foreign interventions that could have unpredictable blowback to the United States was that very phrase – though some reporters have said he has used a more frank term than “stuff”.

Responding to Clinton, one of Obama’s former most senior advisors, David Axelrod, tweeted on Tuesday afternoon, “Just to clarify: ‘Don’t do stupid stuff’ means stuff like occupying Iraq in the first place, which was a tragically bad decision,” he wrote.

This barb was particularly pointed because Obama always opposed America’s invasion of Iraq and that position helped him defeat Clinton in the Democratic primaries.

It has also been reported the President became angry during a private conversation on July 21 with congressional leaders who argued that the President should have armed Syrian rebels.

Obama called the criticism “horseshit” according to a report in the Daily Beast about the conversation.

Days after the meeting one of those in attendance, Senator Bob Corker, wrote an opinion piece in the Washington Post saying, “Today, after three years of bold rhetoric divorced from reality,170,000 Syrians are dead, and we are not innocent bystanders. The President encouraged the opposition to swallow deadly risks, then left them mostly hanging.

“Extremist groups from Syria have surged into Iraq, seizing key territory and resources, and are threatening to completely undo the progress of years of US sacrifice.”

President Obama has said publicly on more than one occasion that he does not believe that arming Syrian rebels could have averted the humanitarian catastrophe. Similarly despite calls from some members of both parties in Congress, the President is still refusing to widen America’s renewed engagement in Iraq beyond defending US personnel in Erbil and supporting Iraqi and Kurdish forces seeking to prevent a genocide of civilians trapped on Mount Sinjar by Islamic State in Iraq and the Levant militants.