Iraqi forces said on Wednesday they had begun to make progress against Islamic State inside a built-up district of Falluja, the militants' stronghold to the west of Baghdad.
The army was previously surrounding Falluja from positions outside the city, which is located 50 km (32 miles) west of Baghdad.
"Our forces have begun in the early hours of the morning progressing in al-Shuhada," a southern neighborhood of Falluja, Sabah al-Numani, a spokesman of the Counter-Terrorism Service, said.
The next target will the central part of the city, he said.
Prime Minister Haider al-Abadi said last week that the army slowed down the pace of the offensive because of fears for the safety of tens of thousands of civilians trapped in the city with limited access to water, food and healthcare.
Iraqi Finance Minister Hoshiyar Zebari said last Friday he expected that the capture of the city would take time as the militants have dug tunnels and planted explosive devices in roads and houses to delay the troops.
"Our forces are now cleaning up the district from the roadside bombs and booby-trapped houses, and then we will hand it over to the police forces to hold the ground," Numani said.
Falluja has been a bastion of the Sunni insurgency that fought both the U.S. occupation of Iraq and the Shi'ite-led Baghdad government.
Islamic State fighters raised their flag there in January 2014 before sweeping through much of Iraq's north and west, declaring a caliphate several months later, from Mosul.
The army started the offensive on May 23, with the backing of Shi'ite militias known as Popular Mobilization Forces (PMF) and air support from the U.S.-led coalition.
Falluja would be the third major city in Iraq recaptured by the government after former leader Saddam Hussein's hometown Tikrit and Ramadi, the capital of Iraq's western Anbar province. Abadi has expressed hope that 2016 would be year of "final victory" over Islamic State, with the capture of Mosul, their de facto capital in northern Iraq.