Britain's Prime Minister David Cameron paid tribute to the United States and Afghan troops killed when Taliban insurgents shot down their helicopter in Afghanistan on Saturday.

"I was deeply saddened to hear of the many U.S. military personnel who lost their lives today in Afghanistan. My thoughts - and the thoughts of the whole country - are with their families and friends," Cameron said in a statement.

Marking the deadliest incident in the decade-long war, 31 U.S. special operation troops - 22 of whom were Navy SEALs from "Team Six" - the unit that carried out the raid that killed Osama bin Laden - were killed when the Taliban in eastern Afghanistan shot down their helicopter, officials said.

Seven Afghan commandos were also killed. According to sources, 22 SEALs from Team Six were killed. It was not immediately clear whether any took part in the raid that killed the 9/11 mastermind.

"They have made the ultimate sacrifice in helping to protect our security, and to build a moer stable and peaceful Afghanistan. We remember, too, the Afghan troops who died alongside them today," Cameron said. "Britain, and our own armed forces serving in Afghanistan, will continue to work steadfastly alongside their U.S. and Afghan colleagues as they help prepare Afghanistan to secure its own territory."

Britain has about 9,500 troops in Afghanistan, making it the second-largest contributor to ISAF after the United States. But Cameron wants all British troops out of a combat role in Afghanistan by 2015.

Responsibility for the helicopter incident was claimed by the Taliban; the crash occurred in Wardak province, just west of the capital, Kabul.

The U.S. official, who spoke on condition of anonymity because he was not authorized to discuss the matter, said the aircraft was most likely brought down by rocket-propelled grenade.

The attack occurred after a night raid, a method that has been praised by American commanders as one of the most effective in the recent military offensive, despite the raids being heavily criticized by Afghan officials and civilians.

NATO confirmed the overnight crash took place and that there "was enemy activity in the area." NATO said it was still investigating the cause, however, and conducting a recovery operation at the site.

"We are in the process of accessing the facts," said U.S. Air Force Capt. Justin Brockhoff, a NATO spokesman.

U.S. President Barack Obama offered his condolences and prayers to the families of the Americans and Afghans who died in the attack, saying their deaths were a "reminder of the extraordinary sacrifice made by the men and women of our military and their families, including all who have served in Afghanistan," Obama said.

"We will draw inspiration from their lives, and continue the work of securing our country and standing up for the values that they embodied," he said.

"We also mourn the Afghans who died alongside our troops in pursuit of a more peaceful and hopeful future for their country."

President Hamid Karzai of Afghanistan also offered his condolences to the victims' families.                       

Karzai's office said in a statement, "The President of the Islamic Republic of Afghanistan has expressed his condolences to the U.S. President Barack Obama and to the families of the victims."

U.S. Defense Secretary Leon Panetta also issued a statement, saying he was "deeply saddened by the loss of many outstanding Americans in uniform and of their Afghan counterparts." Their courage, he said, was exemplary.

Saturday's crash comes as an increase of violence has swept across large portions of Afghanistan, particularly in the east, which has become a flash-point in the conflict as U.S. troops prepare for a phased withdrawal from the country, The Washington Post reported.

Local Afghan officials were quick to point out Saturday that insurgent activity in the volatile Tangi Valley, where the latest helicopter crash occurred, has risen in recent months, since some NATO troops withdrew from a remote base in the area.

"The Americans left because they were getting casualties with each operation ... and since then, the insurgents have increased their activity," said Shahidullah Shahid, a spokesman for the Wardak governor.

In June, Obama announced that all foreign combat forces would leave Afghanistan by the end of 2014; some withdrawals have already begun.

The death toll would surpass the worst single day of lost lives for the U.S.-led coalition in Afghanistan since the war began in 2001. On June 28, 2005, a military helicopter crash in eastern Kunar province killed 16 Navy SEALs and Army special operations troops were killed when their craft was shot down while on a rescue mission for the four SEALs under attack by the Taliban. Three of the four SEALs were killed, and the other injured. It was the highest one-day death toll for the Navy Special Warfare personnel since World War II, The Associated Press reported.

The Saturday crash brings the total number of foreign troops killed in Afghanistan in 2011 to 374, according to the icasualties.org Web-site. Two-thirds of them have been American, including 28 Special Forces soldiers.