(Charles Dharapak/AP Photo)

MANILA - On an Asian trip about asserting American power, President Obama today paid tribute to its greatest symbol: men and women of the U.S. military who serve around the globe, including more than 80,000 in the Asia-Pacific region.

In a speech to U.S. and Filipino troops at Ft. Bonifacio here, Mr. Obama thanked American service members past and present for their sacrifices on behalf of regional security.

He also said a new agreement with the Philippines to send American warships and fighter jets to bases here for the first time in more than 20 years underscores their commitment.

"We'll train and exercise together more to bring our militaries even closer," he told the troops. "We'll improve our ability to respond even faster to disasters like [Super Typhoon] Yolanda."

On a trip to the large American military cemetery here, the president honored U.S. and Filipino service members who fought side by side in the Pacific during World War II and gave their lives.

He laid a wreath and viewed the Tablets of the Missing, which contain the more than 36,000 service members who were killed and never found.

The cemetery is the final resting place for more than 17,000 U.S. war dead from World War II - the largest number of US World War II graves in one place anywhere in the world.

It was a poignant ending to a trip dogged by the crisis in Ukraine, regional conflicts with China, and painstaking negotiations on a new Pacific free-trade partnership. But now, as the latest ABC News/Washington Post poll shows, President Obama has deepening domestic political challenges at home.

Air Force One departed Manila 40-minutes early, racing Obama back to the U.S. to face them.