They said the militants captured Rutba, about 150 kilometres east of the Jordanian border, late yesterday.
Residents were today negotiating with the militants to leave after an army unit on the town's outskirts threatened to start shelling.
The officials spoke on condition of anonymity because they were not authorised to speak to the media.
Rutba is the fourth Anbar town to fall to fighters of the Islamic State of Iraq and the Levant and allied Sunni militants since Friday, dealing a serious blow to Shiite Prime Minister Nouri al-Maliki's government.
The other three are Qaim, Rawah and Anah, as well as a border crossing with Syria.