Military leaders vowed the overall war effort won't be hurt by the downing of a Chinook helicopter by Afghan insurgents that killed 38 U.S. and Afghan troops. The pledge was made Tuesday as the remains of the 30 U.S. troops killed when militants shot down the helicopter Saturday were flown home to Dover Air Force Base in Delaware, the Los Angeles Times reported Tuesday. U.S. Marine Gen. John R. Allen, who assumed command in Afghanistan just weeks ago, honored the slain troops, most of whom were Navy SEALs. In a statement, he said coalition forces would "continue to relentlessly pressure the enemy … and bring lasting and enduring peace to this historic land." "Today, we honor the lives and service of our brave Americans and their valiant Afghan brothers in arms, who fought courageously against the enemies of the freedom and security of both our nations," Allen said in the statement. "In life they were comrades in arms, and in death they are bound forever in this vital cause. We cherish this selfless sacrifice." Allen presided over the solemn ceremony at Bagram airfield near Kabul as the remains were loaded onto two C-17 cargo planes. In Washington, the Pentagon said the arrival of the remains at the military mortuary at Dover AFB would not be open to media coverage. The downing of the helicopter was the largest single loss of military lives during the nearly decade-old war. Twenty-two of those killed were Navy SEALs from the Virginia Beach, Va., Naval Special Warfare Development Group, commonly known as SEAL Team Six -- the same unit that carried out the May 2 raid that killed al-Qaida leader Osama bin Laden. Western military officials confirmed Monday the helicopter had gone down as it was arriving to assist other troops engaged in fierce fighting. Military officials said no casualties were reported among the original ground force in the area, identified as U.S. Army Rangers. Some Western and Afghan officials initially said the helicopter was shot down as it was departing following an engagement with insurgents. The Times said an exact chronology has been slow to emerge in part because of the operational secrecy associated with the units involved. A statement by NATO Monday described an operation that "began as a security search for a Taliban leader responsible for insurgent operations in the nearby Tangi Valley," a gateway to Kabul that has been overrun by Taliban and other insurgent groups in recent months. In Washington, President Barack Obama also spoke of success in Afghanistan Monday. "We will press on, and we will succeed," Obama said. "Our responsibility is to ensure that their legacy is an America that reflects their courage, commitment and sense of common purpose." Defense Secretary Leon Panetta said Monday the deaths were a sobering affirmation of the U.S. "resolve and commitment to complete the mission still at hand." Obama said in June 10,000 U.S. troops would be withdrawn by the end the year and 23,000 more troops by next summer. That would leave about 70,000 U.S. troops in Afghanistan until 2014, the scheduled date for the withdrawal of all foreign forces from the country.