By BEN FELLER

Associated Press

WASHINGTON -- Hours after a personal encounter with the grim cost of war, President Obama said Thursday the sight of 18 flag-covered cases holding the remains of Americans killed this week in Afghanistan can't help but influence his thinking about sending more troops overseas.

"It was a sobering reminder of the extraordinary sacrifices that our young men and women in uniform are engaging in every single day, not only our troops but their families as well," Obama said from the White House, reflecting briefly on his surprise middle-of-the-night trip to Dover Air Force Base to observe the return of the fallen Americans to the United States.

Speaking softly and somewhat haltingly, Obama said losses such as these are "something that I think about each and every day."

Asked whether the somber experience -- watching cases carrying the remains come off a giant C-17 cargo plane one by one in the darkness and meeting privately with families so fresh in their grief -- will affect his overhaul of the U.S. strategy in Afghanistan, the president didn't hesitate to say that it would. But neither did he elaborate.

"The burden that both our troops and their families bear in any wartime situation is going to bear on how I see these conflicts," he said.

By many accounts, it was a difficult night.

After a helicopter ride around midnight to the Delaware base where U.S. forces killed overseas come home, Obama went immediately to a chapel to speak with relatives of the fallen. Their loved ones had died just two or three days before.

Of the 18 fallen Americans on the C-17, 10 of them -- including three Drug Enforcement Administration agents -- were killed Monday when a U.S. military helicopter crashed returning from a firefight with suspected Taliban drug traffickers in western Afghanistan. The other eight soldiers were killed Tuesday when their personnel vehicles were struck by roadside bombs in Kandahar province.

White House press secretary Robert Gibbs said that Obama remained quiet on the way back.

"I don't think you can go out there and not understand what you are seeing," said Gibbs, clearly shaken and moved by the experience. "It's hard not to be overwhelmed."