Iraq's military says its special forces have been deployed around Fallujah as part of an operation aimed at retaking the city from so-called Islamic State (IS) militants.
Meanwhile, Iraqi Kurdish forces have launched more attacks in northern Iraq as part of a strategy aimed at cutting off IS militants who control the city of Mosul.
Dhia Thamir of Iraq's Special Forces Service said the final battalion that is taking part in the Fallujah operation arrived at dawn on May 29 at the sprawling Tariq Camp near Fallujah.
Since that operation began on May 22, Iraqi forces, which include Iran-backed Shi'te militias, have seized control of several areas around Fallujah in Anbar Province.
The predominantly Sunni city is about 70 kilometers from the capital, Baghdad.
Thamir said troops have recaptured 80 percent of the territory around Fallujah since May 22.
He did not comment on the troop numbers or the timing of a planned assault in the city itself.
Fallujah, overtaken by IS militants in 2014, is one of two major Iraqi cities that is under control of the extremist militant group. The other is the city of Mosul in northern Iraq.
The U.S. military has said that some 50,000 civilians remain trapped in Fallujah.
The United States says these residents have been informed by paper leaflets dropped into the city that they should avoid areas close to militant positions and put white sheets on their roofs.
Meanwhile, a powerful Iraqi Shi'ite cleric -- the Grand Ayatollah Ali al-Sistani -- has called on Iraqi forces to protect the civilians trapped in Fallujah.
Speaking through his representative, Sistani said on May 27 that "saving innocent people from harm's way is the most important thing, even more so than targeting the enemy."
IS militants have prevented many of the civilians who remain in Fallujah from leaving the city.
Fallujah was seized by IS militants in January 2014, six months before the extremist group swept across large swaths of territory in northern and western Iraq and in neighboring Syria, declaring a caliphate.
Also in Iraq, Kurdish Peshmerga forces, backed by U.S-led air strikes, announced on May 29 that they have launched a major attack aimed at retaking areas from IS militants to the east of Mosul.
The "Peshmerga-led ground offensive, backed by international coalition warplanes" started before dawn, the security council of Iraq's Kurdish regional government said.
It said the operation involved around 5,500 Peshmerga fighters who were focusing on trying to retake several IS-controlled villages controlled near Khazir, to the east of Mosul.
The Kurdish regional government said the operation was part of ongoing preparations for an eventual assault on Mosul.
Kurdish regional officials said that six hours into the May 29 operation, Pershmerga forces had retaken the village of Mufti.
Peshmerga fighters have in recent months a played a key role in ousting IS from territory and cutting off IS supply routes in northern Iraq.
Aziz Wessi, a Peshmerga commander, said the May 29 attack was ordered by the president of Iraq's autonomous Kurdish region, Massud Barzani.
Wessi told reporters that Peshmerga victory in this operation would help secure the autonomous Kurdish region's capital, Irbil, from danger.
With reporting by AFP, AP, and dpa