Officials said the rebels took two key crossings in Anbar on Sunday, a day after seizing one at Qaim, a town in the province that borders Syria.
The strategically important airport in the northern town of Tal Afar has also reportedly fallen to the rebels.
ISIS-led militants have cut a swathe through parts of Iraq.
Since the fall of Mosul in early June, ISIS – the Islamic State in Iraq and the Levant – have helped win large areas in the west and north.
They have taken four strategically important towns in the predominantly Sunni Anbar province – Qaim, 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.
The capture of frontier crossings could help Isis transport weapons and other equipment to different battlefields, analysts say.
The funeral of a senior army officer who was killed in the fighting for Qaim on Friday was targeted by a suicide and car bomb attack in Ramadi. At least six people were killed as they gathered to mourn Brig. Gen. Majid al-Fahdawi.
Earlier, US Secretary of State John Kerry, speaking in Cairo, singled out ISIS whose “ideology of violence and repression”, he said, “is a threat not only to Iraq but to the entire region”.
Calling it a “critical moment”, John Kerry urged Iraq’s leaders “to rise above sectarian motivations and form a government that is united in its determination to meet the needs and speak to the demands of all of their people”.
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