An American and an Italian held hostage by Al Qaeda were accidentally killed in a U.S. counterterrorism operation earlier this year, the White House said Thursday, in a stunning and tragic admission.

The White House also revealed that two American terror operatives were killed, but the revelation that hostages died -- in an apparent drone strike -- is leading to what President Obama called a "full review."

Obama, speaking from the White House, expressed "grief and condolences" for the deaths of the hostages, American development expert Warren Weinstein and Italian national Giovanni Lo Porto.

“As president and commander-in-chief, I take full responsibility for all our counterterrorism operations -- including the one that inadvertently took the lives of Warren and Giovanni,” Obama said. “I profoundly regret what happened. On behalf of the United States government, I offer our deepest apologies to the families.”

The White House said both men were “accidentally killed” in the operation in January. A senior defense official told Fox News the hostages were killed in a Jan. 14 drone strike.

"No words can fully express our regret over this terrible tragedy," the White House said in a statement.

"The operation targeted an Al Qaeda-associated compound, where we had no reason to believe either hostage was present, located in the border region of Afghanistan and Pakistan," the White House said.

White House Press Secretary Josh Earnest said that compensation payments would be made to Weinstein and Lo Porto's families, though he did not say how much.

The White House revealed that two Americans working with Al Qaeda were killed, as well. Ahmed Farouq, an American Al Qaeda leader, was killed in the same operation in which the hostages died. American-born Al Qaeda spokesman Adam Gadahn was killed in January in a separate incident, according to the White House. Fox News is told he was killed in a drone strike on Jan. 19.

The White House says Farouq and Gadahn were not targeted in the operations, and the U.S. did not have specific information indicating their presence at the sites.

Weinstein, 73, was an American contractor working in Lahore, Pakistan, when he was snatched outside his home on Aug. 13, 2011, by Al Qaeda operatives. The Maryland resident and professor at State University of New York at Oswego was later seen in four "proof-of-life" videos, the most recent of which was released in December 2013. In that video, Weinstein appeared in a tan track suit with a wool cap and pleaded with the U.S. to come to his aid.

"And now, when I need my government, it seems that I have been totally abandoned and forgotten," Weinstein says, apparently reading from a script. "I again appeal to you ... to negotiate my release," he said on the tape.

In a written statement, Weinstein’s wife, Elaine Weinstein, said “there are no words to do justice to the disappointment and heartbreak we are going through.”

“We do not yet fully understand all of the facts surrounding Warren's death, but we do understand that the U.S. government will be conducting an independent investigation of the circumstances. We look forward to the results of that investigation,” she said. “But those who took Warren captive over three years ago bear ultimate responsibility. I can assure you that he would still be alive and well if they had allowed him to return home after his time abroad working to help the people of Pakistan.”

“Warren Weinstein did not have to die,” Rep. Duncan Hunter, R-Calif., said in a written statement. “His death is further evidence of the failures in communication and coordination between government agencies tasked with recovering Americans in captivity – and the fact that he’s dead, as a result, is absolutely tragic.”

Gadahn, 36, the first widely known American to join Al Qaeda, grew up in Orange County, Calif., in a family with Christian and Jewish roots. He converted to Islam at age 17, and began studying Islam at the Islamic Society of Orange County. Gadahn reportedly moved to Pakistan in 1998, where he married an Afghan refugee and later joined Al Qaeda.

In 2001, he cut off contact with his family in California, and in the years following the 9/11 attacks, became a prominent spokesman for the terrorist group, appearing under the name "Azzam Al-Amriki" with Al Qaeda founder and 9/11 mastermind Usama bin Laden in videos justifying and threatening further attacks.

In 2006, Gadahn was placed on the Bureau of Diplomatic Security Rewards for Justice Program list of wanted criminals and indicted by a California federal grand jury on charges of treason.

In a 2007 Internet video called "Al Qaeda Video Warning to U.S. by American Adam Gadahn,” the homegrown radical imposed a list of demands on America, including an end to all support for the “bastard state of Israel.”

“Your failure to heed our demands and the demands of reason means that you and your people will – Allah willing – experience things which will make you forget all about the horrors of September 11, Afghanistan and Iraq."

Fox News' Lucas Tomlinson and The Associated Press contributed to this report.