In the Muslim nation that was his boyhood home, President Barack Obama acknowledged today that U.S. relations are still frayed with the Islamic world despite his best efforts at repair. He urged all sides to look beyond "suspicion and mistrust" to forge common ground against terrorism.

Forcefully returning to a theme he sounded last year in visits to Turkey and Egypt, Obama said, "I have made it clear that America is not and never will be at war with Islam. … Those who want to build must not cede ground to terrorists who seek to destroy."

Beaming with pride, Obama delivered perhaps the most intensely personal speech of his presidency, speaking phrases in Indonesian to a cheering crowd of more than 6,000 mostly young people who claimed him as their own.

For Obama’s standing abroad, the speech was closely watched and consequential, an update on America’s "new beginning" with Muslims that he promised last year in Cairo, Egypt.

"Let me begin with a simple statement: Indonesia is part of me," he said in Indonesian at the University of Indonesia.

He praised the world’s most populous Muslim nation for standing its ground against "violent extremism" and said, "All of us must defeat al-Qaida and its affiliates, who have no claim to be leaders of any religion. … This is not a task for America alone."

Seeking to cement relations with fast-growing Asian trading partners, Obama also paid tribute to the economic dynamism of the region at a time of global financial stress.

"America has a stake in an Indonesia that is growing, with prosperity that is broadly shared among the Indonesian people — because a rising middle class here means new markets for our goods, just as America is a market for yours," he said.

The speech came ahead of a meeting of the Group of 20 major economic powers that begins tonight in Seoul, expected to be marked by trade tensions between the U.S. and major exporting nations such as China and Germany.

Earlier today Obama visited the Istiqlal Mosque, the largest in Southeast Asia. He noted that it was under construction when he lived in Indonesia as a boy from 1967 to 1971.

The president’s brief but nostalgic visit lent an unusually personal tone to the speech, a portion of which was devoted to his childhood here. Obama reminisced about living in a small house with a mango tree out front and learning to love his adopted home while flying kites, running along paddy fields, catching dragonflies and buying such delicacies as satay and bakso from street vendors.

Obama, a Christian who was born in Hawaii, moved to Indonesia at age 6 and lived with his mother, Stanley Ann Dunham, and Indonesian stepfather, Lolo Soetoro. He returned to Hawaii when he was 10 to live with his grandparents.

His homecoming had been twice delayed — first because of the health care legislative battle and then because of the BP oil spill.

Reaching out to the Islamic world, Obama said efforts to build trust and peace are showing promise but are still clearly incomplete.

Obama also praised Indonesia for having "made progress in rooting out terrorists and combating violent extremism."