Hillary "looks forward to hugging it out" with Obama

President Barack Obama embraces Secretary of State Hillary Clinton before delivering a speech on Mideast and North Africa policy in the Ben Franklin Room at the State Department May 19, 2011 in Washington, D.C.

Chip Somodevilla/Getty Images

Amid mounting criticism over her foreign policy remarks, former Secretary of State Hillary Clinton on Tuesday called President Obama to explain that she is not attempting to attack his strategies abroad or his leadership.

"Secretary Clinton was proud to serve with President Obama, she was proud to be his partner in the project of restoring American leadership and advancing America's interests and values in a fast changing world," Clinton aide Nick Merrill said in a statement. "She continues to share his deep commitment to a smart and principled foreign policy that uses all the tools at our disposal to achieve our goals."

Merrill added that in spite of some honest differences of opinion between Clinton and Mr. Obama that "some are now choosing to hype," there is still "broad agreement" between the two leaders on "most issues."

"Like any two friends who have to deal with the public eye, she looks forward to hugging it out when she they see each other tomorrow night," Merrill said, alluding to the party at Martha's Vineyard party that both Mr. Obama and Clinton will attend.

The statement came in response to an interview with The Atlantic magazine in which Clinton said the Obama administration's response to the civil war in Syria has amounted to a "failure."

"The failure to help build up a credible fighting force of the people who were the originators of the protests against Assad--there were Islamists, there were secularists, there was everything in the middle--the failure to do that left a big vacuum, which the jihadists have now filled," Clinton said.

Conservatives were quick to question whether Clinton can legitimately critique the Obama administration's foreign policy, given that she served as the president's top diplomat. Some on the left are also taking issue with her recent remarks.

The liberal grassroots group MoveOn.org on Tuesday released a statement saying that Clinton or any other potential 2016 candidate "should think long and hard before embracing the same policies advocated by right-wing war hawks that got America into Iraq in the first place and helped set the stage for Iraq's troubles today."

"Voters elected President Obama in 2008 to bring the war in Iraq to an end," MoveOn Political Action executive director Ilya Sheyman said in the statement. "MoveOn members will continue to stand with elected officials who oppose military escalation that could put us back on a path to endless war.

In The Atlantic interview, the former secretary of state also said she disagreed with the idea that "don't do stupid stuff" can be a driving foreign policy principle as Obama aides have suggested the president does.

"Great nations need organizing principles, and 'Don't do stupid stuff' is not an organizing principle. It may be a necessary brake on the actions you might take in order to promote a vision," Clinton said.

Former senior White House adviser David Axelrod responded to those particular remarks on Twitter Tuesday: "Just to clarify: 'Don't do stupid stuff' means stuff like occupying Iraq in the first place, which was a tragically bad decision."

Tommy Vietor, the former spokesman for President Obama's National Security Council, told CBS News that the controversy over Clinton's remarks amount to a "tempest in a teapot."

The differences between Clinton's and Mr. Obama's foreign policy views were clear in the 2008 Democratic primary, and once again she laid out her views in her memoir "Hard Choices."

In any event, should Clinton run for president -- and it's not confirmed at this point whether she will -- voters are more concerned with domestic issues, Vietor noted.