KABUL, Afghanistan — Thirty-one U.S. troops, including more than 20 Navy SEALs, and seven Afghan soldiers died when their helicopter was shot down during an overnight operation against Taliban insurgents in eastern Afghanistan, according to statement issued Saturday by Afghan President Hamid Karzai.

Most of the dead were U.S. Navy Seals. It was the worst single-day toll for American forces in Afghanistan since U.S. troops entered that country nearly 10 years ago, and one of the largest tolls in a single incident of either the Afghan war or the fighting in Iraq.

The last time the U.S. military suffered such catastrophic loses was in January 2005, when 30 U.S. Marines and a sailor were killed in a helicopter crash in Iraq's Anbar province; throughout the country, another six U.S. troops died on the ground the same day.

U.S. officials in Afghanistan provided no details, but a senior Pentagon official in Washington confirmed that the helicopter had been shot down and that the helicopter was carrying Navy SEALS. The Associated Press reported the SEALs were from SEAL Team 6, the same unit that provided the troops for the May 2 raid that killed al Qaida founder Osama bin Laden, but that could not be verified independently. The Pentagon released no information on the dead.

That so many of the military's most elite forces could be killed shook troops around the world. It takes years to train a Navy SEAL unit, and however many of those killed on the Chinook were SEALs will have reverberations across the force.

Navy SEALs operate stealthily throughout Afghanistan conducting raids, searches and high-risk operations. Traveling in a group of a dozen or more, they go after high-profile targets or wanted figures, yet they rarely release details on their missions. But in 2008, then-President George W. Bush awarded a Navy SEAL, Lt. Michael Murphy, a Medal of Honor posthumously. He was the first Medal of Honor recipient from the war in Afghanistan.

A villager in the area where the helicopter went down told McClatchy he heard rocket fire. He said he later saw the helicopter burning an orchard about a half-mile from his home.

"Smoke was rising from the helicopter till morning," Mansour Majab said.

In his statement, Karzai said the helicopter went down in Maidan Wardak province, west of Kabul. He expressed his condolences for the deaths to President Barack Obama and the families of the American dead.

President Obama issued a statement from the White House. It read:

"My thoughts and prayers go out to the families and loved ones of the Americans who were lost earlier today in Afghanistan. Their deaths are a reminder of the extraordinary sacrifices made by the men and women of our military and their families, including all who have served in Afghanistan. We will draw inspiration from their lives, and continue the work of securing our country and standing up for the values that they embodied. We also mourn the Afghans who died alongside our troops in pursuit of a more peaceful and hopeful future for their country. At this difficult hour, all Americans are united in support of our men and women in uniform who serve so that we can live in freedom and security."

The Afghan defense ministry confirmed the death of seven Afghan commandos in the crash. Gen. Zahir Azimy, the Afghan army spokesman, placed the crash in Logar province, however.

The Taliban claimed credit for the attack in a statement. "Last night at 11 p.m. in the Joye Zarin area of Tangi Saybabad district, the invader forces conducted a night raid and faced hard resistance from the Islamic Emirate fighters,” according to the statement, attributed to Zabiullah Mujahid, the Taliban spokesman, and posted on the group's website.