MANAMA, Bahrain—The Middle East's wave of popular revolts helped spur the largest street rebellion in years in a Persian Gulf monarchy, and the first to pit a Shiite Muslim majority against Sunni rulers—heightening the dilemma for the U.S. as it struggles to pursue its interests in the region.

The funeral of a demonstrator here Tuesday swelled into growing clashes with security forces amid the gleaming new skyscrapers of this financial capital, which hosts the headquarters...