Backed by sustained air strikes from the US-led coalition, elite troops recaptured the southwestern neighbourhood of Al-Tameem the day before.
The advance was hailed as a significant step in efforts to retake Ramadi, a key IS hub 100 kilometres (60 miles) west of Baghdad, and fragment the jihadists' self-proclaimed "caliphate".
As the counter-terrorism forces that led the offensive prepared their next move, local forces from Anbar province moved in to hold recaptured territory.
The force consists of around 500 fighters, a military source said.
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One of the main tasks for Iraqi forces is to clear the area of bombs planted by IS, a favoured tactic of the jihadists that means they can kill security personnel and civilians long after they have withdrawn from an area.
Cars and trucks laden with tonnes of explosives and driven by suicide attackers were a key weapon in IS's shock capture of Ramadi in mid-May.
A total of four coalition strikes in the area also destroyed IS positions and weapons and impeded the movements of jihadist fighters, the statement said.
Iraqi forces spent months cutting off IS supply lines around Ramadi and slowly closing in on the city by taking suburban areas one after the other.
They now need to make advances on the northern side of the city so they can attack IS from two sides.