Shiite rebels holding Yemen’s president captive in his home reached a deal with the U.S.-backed leader Wednesday to end a violent standoff in the capital, fueling fears that a key ally in the battle against al-Qaida has been sidelined.

The late-night agreement, which promises the rebels greater say in running the Arab world’s poorest nation in exchange for removing its fighters from President Abed Rabbo Mansour Hadi’s residence and key areas of the capital, left unclear who really controls the country.

In the deal, carried on the official SABA news agency, the Houthi rebels also agreed to release a top aide to Hadi that they had kidnapped in recent days. […]