The Yemeni group - known as "al Qaeda in the Arabian Peninsula" - posted the statement this week on a militant Web site that regularly carries al Qaeda messages.
It says the man returned to his home in Saudi Arabia after his release from the U.S. prison at Guantanamo Bay, Cuba about a year ago and from there went to Yemen to join the terror group.
But those reports should not slow the Obama administration's determination to quickly close the facility, according to Rep. Jane Harman.
Harman, a California Democrat, said Friday on CBS' The Early Show that President Barack Obama has to "proceed extremely carefully" in closing the prison.
But she says there is no justification for "disappearing people" in a place outside the reach of U.S. law.
"As President Obama said two days ago, there's a false choice between our safety and our values"
Congressman Pete Hoekstra, of Michigan, the top Republican on the House Intelligence Committee, criticized Mr. Obama's executive order to close the prison as "very short on specifics." Hoekstra, citing a New York Times article, suggested up to 10 percent of released enemy combatants have made their way back to the battlefield to attack American troops.
"The real question that we now face is what is President Obama's strategy to confront this threat from radical jihadists?" Hoekstra told The Early Show.
Hoekstra also questioned the wisdom of transporting detainees to the U.S. to stand trial and, if convicted, to serve prison sentences.
"Why would we want them here and put them in a general prison population and make our hometowns a target for terrorism?"
The Internet statement identified the man as Said Ali al-Shihri and says his prisoner number at Guantanamo was 372.
The posting could not immediately be verified, and Yemen and Saudi Arabian authorities would not immediately comment on it.