WASHINGTON—The White House on Thursday proposed a major program to train and arm moderate Syrian rebels, in a significant expansion of the U.S. role in a civil war that officials fear is bleeding into Iraq and across the region.

The Obama administration requested $500 million—a larger amount than expected—to aid the Syrian opposition, reflecting growing U.S. alarm at the expanding strength of Islamist forces in Syria, who in recent weeks have asserted control of large parts of neighboring Iraq and now pose threats to U.S. allies in the region.

Coming on the heels of a decision to send 300 military advisers to Iraq, the Syrian rebel training elevates the U.S. role in the Middle East.

The proposal amounts to a major U-turn by the administration, which had sought until now to limit its involvement in the war.

However, the expanded U.S. involvement will be on President Barack Obama's terms, by emphasizing the use of partner forces, and not the direct use of American combat forces.