Kabul, Afghanistan (CNN) -- Coalition forces embroiled in a firefight with insurgents in eastern Afghanistan on Saturday had called for assistance but instead had to race to the crash scene of a downed NATO helicopter carrying their reinforcements, officials said Monday.
Everyone inside the CH-47 Chinook was killed, marking the worst single-day loss of American life since the beginning of the Afghan war, NATO reported.
The inbound helicopter -- loaded with 30 U.S. service members, a civilian interpreter and seven Afghan troops -- crashed after being "reportedly fired on by an insurgent rocket-propelled grenade," the statement said.
Twenty-five of those on board were U.S. special operations forces, including 22 Navy SEALs. Five air crew members were also on board.
Two military transport aircraft carrying the remains of the 38 U.S. and Afghan personnel have departed Bagram, Afghanistan, and are headed to Dover Air Force Base in Delaware, Pentagon spokesman Col. David Lapan said Monday. The flights are expected to arrive on Tuesday.
"In life they were comrades in arms, and in death they are bound forever in this vital cause. We cherish this selfless sacrifice," Gen. John R. Allen, International Security Assistance Force commander, said in a statement. He pledged to continue the fight in Afghanistan.
"Today, as we pay our respects to these magnificent troops, we recommit ourselves for the future and for the freedom, peace and stability of Afghanistan," he said.
Because the catastrophic nature of the crash made the remains difficult to identify, all 38 sets are being taken to the United States. The Afghan remains will be returned to their families once identifications can be made.
"Their loss is a stark reminder of the risks that our men and women in uniform take every single day on behalf of their country," U.S. President Barack Obama said Monday. "Day after day, night after night, they carry out missions like this in the face of enemy fire and grave danger."
Obama said he has spoken with U.S. military officials in the field and with Afghan President Hamid Karzai. "We will press on and we will succeed," he said. But the president added that "now is also a time to reflect on those we lost" and on the sacrifices of all who have served, as well as their families.
The president discussed the incident at the end of televised remarks focused on the economy.
U.S. Defense Secretary Leon Panetta, speaking earlier, said, "The thoughts and prayers of the entire nation are with the families and with the loved ones of those we lost in Afghanistan over the weekend. They were far from home, but we know that they were also where they wanted to be.
"As heavy a loss as this was, it would even be more tragic if we allowed it to derail this country from our efforts to defeat al Qaeda and deny them a safe haven in Afghanistan," Panetta added. "Instead, we will send a strong message of American resolve from this tragedy, we draw even greater inspiration to carry on the fight."
Until Monday, military officials had been largely tight-lipped about the circumstances surrounding the crash, which occurred in the rugged Tangi Valley area of Wardak province, about 60 miles southwest of Kabul.
The events leading up to the crash began when insurgents -- armed with rocket-propelled grenade launchers and AK-47 assault rifles -- engaged in small-arms fire with coalition forces on the ground, NATO reported. ISAF forces were carrying out an operation targeting a known Taliban leader in the area.
Several militants were killed in the gun battle, officials said. Coalition troops called in additional forces to assist in the operation as the firefight continued.
"Those additional personnel were inbound to the scene when the CH-47 carrying them crashed, killing all on board," NATO said.
The troops on the ground immediately left the scene of the insurgent firefight "to secure the scene and search for survivors."
NATO spokesman Brig. Gen. Cartsen Jacobsen said the crash site has been cordoned off, while recovery efforts continue.
An investigation is under way, he said.
"The recent fighting season has not materialized as the insurgents had predicted," Jacobsen told reporters in Kabul. "But the insurgents are resilient and far from defeated."
Jacobsen told reporters there was no indication of newer, more sophisticated weapons, responding to rumors that Taliban insurgents may have been the beneficiaries of better equipment during the exchange.
Saturday's crash represents the second downed NATO helicopter by insurgent fire in recent weeks. A helicopter was shot down in eastern Afghanistan in July, though no casualties were reported.
Despite Saturday's loss, Afghan and NATO operations do not appear to have relented.
On Monday, more than 100 demonstrators in Ghazni province protested what they say is the killing of two people during a NATO raid, according to provincial council chief Hamid Ullah Nawroz.
ISAF spokesman Capt. Justin Brockhoff confirmed that there was a joint Afghan-NATO raid late Sunday evening in the area that killed two insurgents, uncovered a munitions cache and detained "numerous suspected insurgents."
Meanwhile, NATO says one of its helicopters made a hard landing Monday in southeastern Afghanistan.
The Navy transport helicopter went down in Paktika province, though "initial reporting indicated there was no enemy activity."
No casualties were reported.
CNN's Barbara Starr contributed to this report.