The rebels, who include
Islamic State in Iraq and the Levant (Isis)fighters, now control three border crossings in Anbar province, Iraq's largest.
Meanwhile, in the north, reports say the airport in the town of Tal Afar has also fallen to the rebels.
The militants' gains in large parts of western and northern Iraq have alarmed the international community.
They have taken four strategically important towns in the predominantly Sunni Anbar province - Qaim, on the Syrian border, and Rutba, Rawa and Anah - in the last two days.
Gunmen reportedly captured the border posts of al-Waleed, on the Syrian frontier, and Turaibil, on the Jordanian border, on Sunday after government forces pulled out.