"Currently there are 13 killed in action and more than 20 wounded," the U.S. military said in a statement.
The wounded have all been transferred to medical facilities and authorities are searching for more survivors, it said.
The Chinook helicopter was believed to be carrying dozens of soldiers to their leaves abroad when it was struck by a missile and crashed in corn fields west of Baghdad, witnesses and U.S. officials said. A coalition official had earlier said that at least two soldiers were killed and 20 injured.
Witnesses south of Fallujah, 40 miles west of the capital, said they saw two missiles fired at the helicopter, which came down near the village of Hasi, six miles to the south. Fallujah is a center of Sunni Muslim resistance to the U.S. occupation.
"The Chinook was shot down by an unknown weapon," a U.S. military spokesman in Baghdad said on condition of anonymity.
American military officials have repeatedly warned that hundreds of shoulder-fired surface-to-air missiles remain unaccounted for in Iraq since the collapse of Saddam Hussein's regime in April. Insurgents have fired on U.S. aircraft before, but this was the first known shootdown involving the Baghdad airport.
Across Iraq, it was the third helicopter known to have been brought down since President George W. Bush declared an end to major combat on May 1.
The helicopter was part of a formation of two Chinooks carrying more than 50 passengers to the U.S. base at the former Saddam International Airport, renamed Baghdad International.
"Our initial report is that they were being transported to BIA for R&R flights," that is, rest and recreation leaves abroad, a U.S. command spokeswoman in Baghdad said. She said at least some were coming from Camp Ridgeway, believed to be an 82nd Airborne Division base in western Iraq.
Witnesses said the second copter hovered over the down craft for some minutes and then set down, apparently to try to help extinguish a fire, but the downed copter was destroyed.
At least a half-dozen Black Hawk helicopters later hovered over the area, and dozens of soldiers swarmed over the site. Injured were still being evacuated at least two hours later.
Local villagers displayed blackened pieces of wreckage to arriving reporters, and in nearby Fallujah townspeople celebrated on the streets.
In other developments:
The U.S. military said two U.S. soldiers from the 101st Airborne Division were killed and two wounded in the roadside bombing in Mosul.
The two deaths would bring to 122 the number of American soldiers killed by hostile fire since President Bush declared an end to combat on May 1 when added to the total given by the Department of Defense on Friday. A total of 114 U.S. soldiers were killed between the start of the war March 20 and the end of April.
It was a street leaflet attributed to the fugitive ex-president Saddam's Baath Party that called for a three-day general strike and declared Saturday a "Day of Resistance," sparking rumors of planned new terror bombings.
This came just days after four coordinated suicide bombings in Baghdad last Monday killed about three dozen people and wounded more than 200, almost all Iraqis.
Despite these fears, many shops in this city of 5 million people opened Saturday as usual, although fewer Baghdadis seemed willing to venture out in the morning. Traffic picked up as the day wore on, however, and as people realized no siege of bombings had materialized.
Police checkpoints had been set up across the city. "I went out as usual and sent my children to school," said one resident, Karima Dawth. "Warnings by Baathists don't terrify us."
Most parents seemed to feel otherwise, however, as schools reported very low attendance.
In Iraq's second- and third-largest cities, Basra and Mosul, there was no sign of strike action. Shops were open and traffic appeared normal.
The "Day of Resistance" threat had prompted some Western governments to issue warnings to their citizens here. The U.S. authorities urged Americans to "continue to maintain a high level of vigilance," since the vague threats seem to cover a two- or three-day period.
"There's no denying this has been a tough week," Bremer said at the start of Saturday's news conference. He noted it began with a rocket attack a week ago on Baghdad's Al Rasheed Hotel, home to hundreds of staff members of his Coalition Provisional Authority. The barrage killed a U.S. Army colonel and wounded 18 other people.
The following day, four near-simultaneous suicide bombings killed about three dozen people and injured about 200 in the capital, prompting the international Red Cross, the United Nations and other organizations to withdraw foreign staff.
U.S. officials have blamed former Baath Party figures, foreign fighters and Islamic extremists for the upsurge in attacks.
Bremer told reporters that capturing or killing Saddam was a "top priority" of the coalition forces, but he dismissed recent reports that the ousted leader is taking a strong role in organizing the anti-U.S. resistance.
"We have no clear indication that Saddam himself is behind these attacks," he said. "There is some sign of control over these attacks at a regional level."
Bremer said the coalition, once it gets additional money from Congress, will accelerate the building of the new Iraqi army, police and other security forces.
"This is after all their country," Bremer said. "It is their future."
He said the coalition will double the size of the Iraqi Civil Defense force by March, and accelerate the recruitment and training of more Iraqi police and soldiers.
Bremer said he hoped to make quick progress with the U.S.-created Iraqi Governing Council on the first key step to handing over sovereignty to Iraqis, a decision on how to draw up a new constitution.
Bremer also said the Americans would "seek ways to accelerate the transfer of authority to the government of Iraq for the governance to Iraqis."
He said he hoped to make quick progress with the U.S.-created Iraqi Governing Council on the first key step, a decision on how to draw up a new constitution. "We are prepared to provide a path and a timeline with the Governing Council," he said.