"I met with the Joint Operations Command and they confirmed to me that we will regain all of the city of Ramadi by the end of this month," Khaled al-Obeidi told reporters in Baghdad.
Earlier this month, forces led by Iraq's elite counter- terrorism service retook Al-Tameem, a southwestern neighbourhood of Ramadi from the Islamic State group.
IS took full control of Ramadi in mid-May, in what was Baghdad's most stinging defeat since it launched a counter- offensive to regain the large regions the jihadists captured in the summer of 2014.
"The reason the battle took so long was to avoid casualties among our forces and also to avoid civilian casualties," Obeidi said. "There are still many civilians in the city."
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Jihadists still holed up in the city centre and using tunnels to avoid air strikes may number no more than 300, according to military officials.
IS fighters attacking from northwest of Ramadi with suicide car bombs attempted to retake control of the key Palestine bridge in recent days but Iraqi forces still have the upper hand.
He said that IS had been using the Euphrates river that runs through Ramadi to supply its fighters inside the city with men and military equipment.
Control of both sides of the river banks in key areas have significantly reduced the jihadist organisation's ability to re-supply, Warren said.