Ben Smith, a former Navy SEAL and spokesman for the supposedly bipartisan Special Operations OPSEC Education Fund, made the claim on his Facebook page shortly after the president's State of the Union address in January.
Smith also said the president was "an impostor," a Muslim and a "Manchurian candidate" who should "go back to the country you were born in," according to the post.
In previous posts, Smith noted the Obama administration was in the process of building a "caliphate through the incrementalism of Socialism," using to the term favored by al Qaeda and other terror groups regarding the establishment of a new worldwide Islamic empire.
Such comments underscore the fund's recent efforts to discredit the Obama administration's defense and national security bona fides.
The group, which is reportedly tied to Republican and Tea Party groups, issued a video charging the Obama administration with leaking details of sensitive national security operations and of using the mission targeting former al Qaeda leader Osama bin Laden for political gain.
“We have become a political weapon — we are not,” Smith says in the video. “Our job is to be silent professionals — we do not seek recognition; we do not seek popularity ... to make things public is wrong."
Democratic Sen. John Kerry (Mass.) compared the fund's efforts to those he faced by a group of Vietnam veterans who openly questioned the Democratic senator’s war record during Kerry's failed White House bid in 2004.
"Seeing the new outrageous attacks made against President Obama from a shadowy Republican-allied veterans group called OPSEC ... remind me all too well of the notorious 'Swift Boat' attacks I faced in the 2004 campaign," Kerry said in the statement.
"I honor and appreciate the service of my fellow veterans, but a false attack is a false attack — no matter who’s making it," he added.
OPSEC Fund opponents have fired back against the group's claims, taking particular aim at Smith.
In a website titled "Who is former Navy SEAL Benjamin Smith," opponents highlighted Smith's Facebook comments questioning Obama's citizenship, faith and political alignment.
Responding to the caliphate reference, the site suggests Smith adheres to "communist, one world government" conspiracy theories advocated by far-right ideologues such as Glenn Beck and others.
On Monday, Smith responded to the site's accusations, posting on his Facebook page that he is not a so-called birther but "I have my doubts like the rest of us," over the president's citizenship status.
Foreign Policy first reported details of Smith's Facebook postings on Monday.