Iraqi government forces fighting to retake Fallujah from the Islamic State group seized a southern neighbourhood of the city on Wednesday, officials said.
Led by the country's counter-terrorism service, Iraqi forces and allied militias backed by air support from a US-led coalition began an operation on May 23 to wrest the city from IS.
Iraqi forces made incursions into Fallujah, 50 kilometres (30 miles) west of Baghdad, in the early days of the offensive, but their advance soon slowed.
They managed last week to enter parts of the southern neighbourhood of Al-Shuhada Al-Thaniya and on Wednesday took full control of the district, Sabah al-Noman, the spokesman for the counter-terrorism service, told AFP.
"Counter-terrorism service forces liberated Al-Shuhada Al-Thaniya entirely from Daesh control and raised the Iraqi flag over buildings in the district," he said, using an Arabic acronym for IS.
"The army and the police will be responsible for controlling the neighbourhood after it has been cleared of bombs," Noman said.
A colonel in the Anbar province police force confirmed government forces took control of the district and said five members of the security services were injured during fighting on Wednesday.
Lieutenant General Abdelwahab al-Saadi, who is commanding the operation, said on Tuesday that Iraqi forces were advancing on the centre of the city from the south and vowed that "within the coming days we will announce the liberation of Fallujah."
Jasim Al-Halbous, a member of the Anbar provincial council, said the taking of the district was an important strategic victory.
"Al-Shuhada Al-Thaniya is the largest neighbourhood in southern Fallujah and its liberation marks the launch of a rush by security forces for the centre of Fallujah," he said.
"Daesh fighters were hiding in fortified tunnels and various houses in the district."
Fallujah is one of the most important bases of IS -- which seized control of large parts of Syria and Iraq in mid-2014 -- and the second-largest city in Iraq still under the jihadist group's control after Mosul.
Fallujah was the first Iraqi city to fall out of government control in January 2014 and was the scene a decade earlier of some of the worst fighting US forces had seen since the Vietnam War.
The Iraqi advance on the city comes as IS is also under pressure in Syria from twin offensives by US-backed Arab and Kurdish fighters and regime troops supported by Russia.