BEIRUT — Syrian rebels captured most of an eastern oil field and stormed a military base in the south, antiregime activists said Thursday, further chipping away at President Bashar Assad’s hold on the country’s hinterlands.

Although Assad’s regime does not appear on the brink of collapse, rebels seeking his ouster have scored a string of strategic victories during the past week, also seizing a large dam and the defenses around a major airport. These blows have shrunk the portion of the nation that Assad effectively governs and may deprive his regime of needed resources.