BAGHDAD—Iraq's government sent its air force on Monday to back Kurdish forces struggling to blunt a jihadist advance, an extraordinary move that reflects alarm over the insurgents' brash new offensive against Kurds in both Iraq and Syria.

Prime Minister Nouri al-Maliki's authorization of air support came after the Kurdish forces, known as Peshmerga, lost a string of towns over the weekend to the militant group, which calls itself Islamic State. The Peshmerga had held off the insurgents in northwestern Iraq without central Iraqi...