The inroads came after Iraqi troops, counterterrorism unit members and federal police officers targeted ISIS militants from three sides in a 24-hour period, aided by U.S.-led airstrikes.
Iraq's Joint Military Command reported 60% of the Anbar province city had been retaken, including a one-time Iraqi military headquarters in northern Ramadi, as well as western and southern parts of the city.
Dozens of ISIS fighters died in the operation, according to the military. It wasn't immediately clear if there were any Iraqi casualties. Iraqi troops also managed to confiscate a large amount of weaponry.
U.S. Central Command said it had launched six strikes Monday around Ramadi, hitting two ISIS tactical units and destroying weaponry, ammunition and supply caches, buildings and a vehicle.
Besides its strategic significance, Ramadi -- some 120 kilometers (75 miles) west of Baghdad in the Sunni heartland -- has symbolic importance in Iraq's fight against ISIS.
Iraqi forces withdrew en masse from the city in May
, a pullout regarded as a huge setback to the anti-ISIS campaign, and spurred U.S. Defense Secretary Ash Carter to question
whether the Iraqis lacked the "will to fight."
Iraqi officials, including Prime Minister Haider al-Abadi, later said Carter had bad information. And Salim al-Jabouri, speaker of the Iraqi parliament and arguably the country's most powerful Sunni politician, said that even the Prime Minister
didn't know of the withdrawal until after it happened.
The city was one of "three R's" identified as the core of a triple-pronged U.S. strategy against ISIS that Carter floated before U.S. lawmakers in October
. The others were raids by special forces, and Raqqa, the extremists' de-facto capital in Syria.
ISIS tries to keep residents from fleeing
This embarrassment has made retaking Ramadi a focus for Iraqi forces, who have been battling ISIS on several fronts. The terror group has taken over vast swaths of Iraq and neighboring Syria while creating what it calls the Islamic State in addition to inspiring and carrying out attacks elsewhere.
Starting last month, Iraqi forces began dropping leaflets on Ramadi urging people to leave ahead of a promised military offensive.
"To our people in the city of Ramadi, evacuate your families from the city immediately and go to the south through al Hameera area," the leaflets read, according to the Iraqi military.
But leaving isn't necessarily easy. Ramadi residents told CNN on Monday night that ISIS had set up additional checkpoints around the city to prevent people from fleeing.
"Daesh made it very clear to all of us that anyone who tries to flee the city will be considered an apostate. And you know what they will do to an apostate," said one resident, referring to ISIS' practice of detaining and killing those who don't accept its extreme ideology.
Another told CNN that most people were unable to leave due to the threat of being caught fleeing by ISIS.
"(I'm) not going to take the risk," he said. "The government is not proving us any guarantees that we will be safe during our trip south."
U.S. wants Iraqis to 'move as rapidly as possible'
The Iraqis began pushing last spring, right after Ramadi fell. That didn't yield immediate results.
In October, Col. Steve Warren, a spokesman for the U.S.-led anti-ISIS coalition, told reporters
that "we now believe the battlefield conditions are set" for Iraqi forces to take back Ramadi.
At that point, Iraqi forces had established positions in the city's suburbs, he said.
"We'd like to see them move as rapidly as possible," Warren said then. "We believe now is the time for the final push into Ramadi."
Tensions simmer over Turkish troops
The assault on Ramadi came amid increasing tensions between Iraq and Turkey over Turkish forces stationed near Mosul, another ISIS-held Iraqi city.
The troops arrived with armored vehicles Thursday at a camp in territory held by Iraqi Kurds near Mosul, Iraq's second-largest city.
Turkey has said the troops are there to protect a mission to train and advise Iraqi forces in their fight against ISIS. It said the forces have been operating in the region at the request of Iraq's government.
But Iraq's government insists that it never invited the Turkish forces and that their presence constitutes a violation of Iraqi sovereignty.
Abadi, Iraq's Prime Minister, spoke on the phone Tuesday with NATO Secretary-General Jens Stoltenberg, rejecting the presence of the Turkish troops and calling for them to withdraw immediately, according to a statement from Abadi's office. Turkey is a member of NATO.
Abadi also spoke to Massoud Barzani, president of the Kurdistan Regional Government in Iraq that governs over a semiautonomous region in Iraq's north, about the presence of the Turkish troops, according to a statement from the Prime Minister's office.
Barzani had "stressed that Iraq's sovereignty is a red line for us" and that his government stood with anyone who helped in the fight against ISIS, but not without the preservation of sovereignty, according to the statement.
Three Turkish bases in Iraq
The Kurdistan Regional Government said Saturday that Turkey had opened three military training bases in Iraq in late 2014 -- two for Kurdish Peshmerga forces in the Kurdish region's Soran and Qalacholan districts and a third for other Iraqi forces near Mosul. Military and logistical equipment had been transferred to the Mosul base in recent days to expand its capacity, a statement said.
Turkish Foreign Minister Mevlut Cavusoglu said Monday that Turkey has a duty to protect its soldiers around Mosul, according to Turkish state broadcaster TRT. But the country would halt sending troops to Iraq, the country's semiofficial Anadolu Agency reported over the weekend, citing Prime Minister Ahmet Davutoglu.
He also expressed that Turkey would continue to support Iraq's fight against ISIS, according to the report.