Since leaving the State Department last year, Hillary Rodham Clinton has racked up scores of accolades and appeared on many a big stage. Still, it might come as a surprise that a past Republican presidential nominee -- specifically, the one who is among the loudest critics of Clinton's handling of the Benghazi terrorist attacks -- would invite her to his desert retreat for a lofty conversation about leadership values.

This is precisely what Sen. John McCain (R-Ariz.) has done.

Clinton, a prospective 2016 Democratic presidential candidate, will appear on stage Saturday with McCain at the Sedona Forum, an annual ideas festival hosted by the McCain Institute for International Leadership at Arizona State University. Clinton is among the national and international business leaders, philanthropists and public figures appearing at the gathering, held in Sedona, the tony red-rocks oasis in Arizona's Verde Valley.

In a statement released Thursday, McCain called Clinton "my friend" and praised her public service career.

"From her years of service as first lady, in the U.S. Senate and the State Department, one would be hard-pressed to find a leader with Secretary Clinton's informed perspective on the many challenges facing America across the globe," McCain said.

According to a news release, Clinton is scheduled to "participate in a conversation" with McCain. This year's forum will focus on "Crisis in the Middle East: Values, Strategy and Options," and will include a session on Russia and Ukraine and on combating human trafficking.

McCain, along with Sens. Lindsey O. Graham (R-S.C.) and Kelly Ayotte (R-N.H.), has been a consistent critic of Clinton's handling of the Sept. 11, 2012 attacks in Benghazi, Libya, when four Americans, including U.S. Ambassador to Libya J. Christopher Stevens, were killed. 

Clinton repeatedly has taken responsibility for what happened in Benghazi. At an event in Boston on Wednesday, Clinton said of the incident, "It's very painful and it was certainly the biggest regret that I had as secretary of state."

Clinton and McCain forged a friendship in the Senate, when both served on the Armed Services Committee, and they and their spouses have supported each other's philanthropic endeavors.

Last month, McCain appeared on stage with Bill Clinton at the Clinton Global Initiative University conference in Tempe, Ariz., hamming it up like old buddies. And this week, Cindy McCain appeared at an event in Phoenix with business and community leaders and to promote Too Small to Fail, the early childhood education initiative that Hillary Clinton is helping lead. McCain sits on the group's leadership council.