Iraqi forces took up positions around the capital of the majority-Sunni province of Anbar on May 27, seizing two districts after clashes with Islamic State (IS) fighters.
Iraqi forces fought militants on the southern outskirts of Ramadi, which the IS seized on May 17.
An army colonel said Iraqi troops and Shi'ite militia fighters moved into the districts of Taesh and Humeyrah and also entered the neighboring Anbar university compound.
The areas recaptured by the Iraqi forces are outside the main road circling the city from the south.
An assault to retake Ramadi has not started in earnest.
Meanwhile, an Iraqi army spokesman said that a wave of IS suicide bombings targeted the Iraqi Army outside the Islamic State-held city of Fallujah late on May 26, killing at least 17 troops.
In Syria, a monitoring group said Kurdish forces retook 14 Assyrian Christian villages the militants had seized in February.