Iraq has quietly started negotiations to buy U.S. fighter jets and air-defense systems worth billions of dollars, a purchase Washington hopes will help counter Iranian influences and cement long-term ties with Baghdad after American troops pull out.

Baghdad had frozen plans to buy 18 advanced U.S. F-16 fighters earlier this year after the Arab Spring protests in the region turned its attention to internal stability. Now, senior U.S. and Iraqi officials said Iraq is considering raising its purchase to as many as 36 of the...