An interpreter also died when the Chinook helicopter plummeted after a firefight with insurgents during an anti-Taliban operation late Friday in Wardak province, southwest of the capital Kabul.
The crash site had been sealed off by Sunday, with reports that fighting was still going on in the area where a rocket propelled grenade (RPG) is thought to have downed the troop-carrying aircraft.
The incident was the biggest single loss of life for foreign forces since an American-led invasion of Afghanistan toppled the Taliban from power in 2001.
(Read: Afghan insurgency: A decade on, NATO troops face deadliest day)
A witness said the helicopter crashed after a raid on a Taliban commander's home.
"Afghan and foreign troops are still in the area," provincial spokesman Shahidullah Shahid told AFP on Sunday, noting that phone coverage had been blacked out.
"The area is sealed off and we have reports of sporadic fighting," he said.
The Taliban had claimed responsibility for the attack. Local and Afghan army officials said an insurgent rocket had brought the helicopter down.
The NATO-led ISAF (International Security Assistance Force) mission in the troubled country, confirmed an investigation was under way to determine the exact circumstances of the crash.
The aircraft was said to have broken into several parts after being hit by the rocket. "The operation of recovery is ongoing," ISAF added in a statement, referring to efforts to reclaim the Chinook wreckage.
An ISAF spokesman would not comment on what attempts were being made to recover the bodies of those killed.
US President Barack Obama paid tribute to the troops who died and said the incident was a reminder of the "extraordinary sacrifices" made by the men and women of the military and their families.
Defense Secretary Leon Panetta vowed the US would "stay the course" in Afghanistan despite the latest loss.
Some foreign troop withdrawals have already begun as part of a transition that has already seen Afghan security forces, whose abilities are disputed, take control of key regions this summer.
Afghan President Hamid Karzai's office was first to officially release the death toll on Saturday and he offered condolences to the victims' families.
US television networks reported that 25 of the dead in Friday's attack were US Navy SEALs. Sources in the Obama administration told AFP that those killed came from the army, navy and air force, without saying if they were SEALs.
The previous single biggest death toll in Afghanistan saw 16 American soldiers killed in 2005 when a Taliban rocket hit their Chinook in the eastern province of Kunar.
The defence ministry in Kabul said the seven Afghan soldiers who died were members of an elite commando unit.
A total of 342 foreign troops -- 279 from the United States -- have now been killed in Afghanistan this year, according to an AFP tally based on the independent website iCasualties.org.
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A MANPAD downed that Chinook. The only way Taliban/Afghan insurgents can get their hands on one is if Iran or Pakistan gave them one. What will happen next is anybody's guess.