The Taliban claimed responsibility in a phone call.
The US military said on Tuesday that the fate of those on board was not immediately known, but the twin-rotor helicopter can carry up to 35 crew and troops.
The Chinook was transporting soldiers into an area in support of US forces, the military said in a statement. "The cause of the crash and status of survivors is unknown at this time."
Provincial Governor Asadullah Wafa told The Associated Press that the Taliban downed the aircraft with a rocket. He gave no other details.
Purported Taliban spokesman Mullah Latif Hakimi called the AP before news of the crash was released and claimed that the rebels shot the helicopter down.
Hakimi often calls news organizations to claim responsibility for attacks on behalf of the Taliban. His information has sometimes proven untrue or exaggerated, and his exact tie to the group's leadership is unclear.
Hours earlier, a top policeman and his two sons were killed after a bomb destroyed their vehicle south of Kunar province's capital city. Seven others were also wounded.
Another roadside bomb killed two police officers and wounded two others in the Naish district of the southwestern province of Kandahar, police said.
But the government said fighting in the southwest last week showed the weakness of the Taliban, ousted from power by US-led forces in late 2001.
It added that Afghanistan's US-backed forces had killed 178 suspected Taliban in the Mian Nishin region in what would be one of the fighters' bloodiest setbacks, although US forces gave a toll of 77.
"The events in Mian Nishin show how fragile the terrorist threat against the people of Afghanistan is," said government spokesman Jewad Ludin.
"(The guerrillas) are very small compared with the increasing capability of our own forces, compared with the combined capability of the international community that's there to help us and compared to the will of the Afghan people."
However, a Taliban spokesman told Aljazeera.net on Thursday that its forces had never been in Mian Nishin and that the suspected Taliban must have been civilian tribesmen.
Election office hit
Meanwhile, rockets struck a UN election office in Asadabad but the government reacted by saying Taliban guerrillas would not derail parliamentary polls and that the rockets had not caused casualties or damage.
Ludin vowed the parliamentary elections would be held on time on 18 September. "The (Taliban) challenges are very feeble," he said.
On Saturday helicopters flew the
bodies of two Germans home
Election organisers said on Monday a voter registration drive had produced an overwhelming response, with 73,000 people signing up in two days.
But UN Special Representative Jean Arnault told the UN Security Council on Friday the worsening security had had a negative impact on poll preparations and military operations were not enough to beat destabilisation efforts by the Taliban.
He said it was necessary to stop Taliban financing, safe havens and support networks and welcomed contacts on this with neighbouring Pakistan, which Afghan and US officials have accused of giving sanctuary to guerrillas despite being an ally in the US-led war against terrorism.
About 400 insurgents have been killed since March, according to government and US figures. Fourteen US troops and dozens of Afghan police and troops have been killed in attacks.