Iraqi forces have recaptured several areas in west Mosul since launching the push to retake it on February 19, but their pace slowed recently amid several days of wet weather, which makes air support more difficult.
West Mosul is the largest urban population center still held by the Islamic State group.
The fall of west Mosul would effectively mark the demise of IS's cross-border "caliphate," which its leader Abu Bakr al-Baghdadi announced from a mosque in the city in 2014, but the threat posed by the jihadists would still be far from over.
"Federal police and Rapid Response Division forces are attacking Al-Dindan and Al-Dawasa neighborhoods," Iraq's Joint Operations Command said.
Al-Dawasa includes the Nineveh governor's headquarters and other government buildings.
The Iraqi army is also taking part in the fight for west Mosul, with the 9th Armoured Division advancing through the desert surrounding the city, aiming to cut it off from the IS-held town of Tal Afar, further west. More than 45,000 people have fled west Mosul since the push to retake it began, while more than 200,000 are displaced because of the battle for the city, says the International Organization for Migration.