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Lieberman will serve as co-chairman of the American Internationalism Project, alongside former Sen. Jon Kyl (R-Ariz.).

"The American Internationalism Project, under the leadership of Sen. Lieberman and Sen. Jon Kyl, is critical to opening a discussion about the challenges facing America in the coming decades — and strategizing about how to meet them," AEI president Arthur C. Brooks said in a statement.

Lieberman, who opted in 2012 not to run for reelection, said there is currently an "urgent need to rebuild bipartisan — indeed non-political — consensus for American diplomatic, economic, and military leadership in the world."

"That's why I am grateful to AEI for initiating and sponsoring this project and why I look forward to leading it with my friend Jon Kyl," Lieberman said.

Roughly a week ago, AEI announced that Kyl had joined the American Enterprise Institute as a visiting fellow. Kyl also retired from the Senate in 2012.

Lieberman, formerly the chairman of the Senate Homeland Security and Governmental Affairs Committee, was one of the chief architects of a comprehensive cybersecurity bill that failed to pass the Senate last year. 

Despite the gridlock, Lieberman has continued his call for Congress to pass cybersecurity legislation to help protect American critical infrastructure from cyberattacks. 

Lieberman was former Vice President Al GoreAlbert (Al) Arnold GoreKeep calm and let the election officials carry on Fox News president warns of calling winner too soon on election night: 2000 still 'lingers over everyone' Older voters helped put Trump in office; they will help take him out MORE's Democratic running mate when Gore ran for president in 2000. Lieberman served as a Democrat until 2006 when he faced a primary challenge from businessman Ned Lamont. Lieberman eventually won reelection as an Independent in that race.

In 2008 Lieberman endorsed Sen. John McCainJohn Sidney McCainObama book excerpt: 'Hard to deny my overconfidence' during early health care discussions Mark Kelly releases Spanish ad featuring Rep. Gallego More than 300 military family members endorse Biden MORE's (R-Ariz.) presidential candidacy and spoke at the Republican National Convention. Lieberman caucused with Democrats in recent years.

—Jennifer Martinez contributed reporting.