American-backed Iraqi forces erected a makeshift floating bridge across a branch of the Euphrates River on Tuesday and began pushing troops and vehicles into Ramadi's city center.
"The fall of Ramadi is inevitable. The end is coming," Army Col. Steve Warren, a U.S. Defense Department spokesman in Baghdad, said Tuesday.
But "there is still a long way to go before we can declare Ramadi is completely clear. There is a lot of dense terrain here that needs to be negotiated," Warren said in a press briefing.
The Iraqi army used an "improved ribbon bridge" provided by the U.S. military that allows Iraqi infantry units to cross the Tharthar Canal and move vehicles and combat equipment into the dense urban areas that Islamic State militants have controlled since May, Warren said.
Successfully seizing Ramadi would be one of the Iraqi army's biggest battlefield victories since Islamic State militants overran large swaths of the country in June 2014.
Estimates suggest about 250 to 350 fighters remain inside the city center and another several hundred are scattered elsewhere in the area surrounding Ramadi, Warren said.
The Iraqi soldiers "are encountering booby traps, [improvised explosive devices], and the presence of enemy fighters who are fighting fairly hard. The numbers aren't really high, I would say, but in that restricted terrain … it's not very easy to maneuver through that terrain so it doesn't take much in the way of defense capability … to hold them back," Warren said.
The several hundred U.S. troops deployed to Anbar province remain inside the wire at Taqqadem Air Base about 25 miles from Ramadi providing advice to senior Iraqi leaders and authorizing airstrikes to support the Iraqi units' fighting.
The Iraqi government declined a recent offer from the United States to provide additional combat advisers and attack helicopters for the final phase of the Ramadi operation.
The mostly Shiite Iraqi army is leading the invasion of Ramadi, a Sunni Muslim city. Several thousand Sunni tribal fighters and Sunni policemen are standing by to secure the city after the soldiers clear our the Islamic State fighters, Warren said.
On Monday, Iraqi Prime Minister Haider al-Abadi reiterated his reluctance to allow U.S. ground troops to join the fight.
"We don't want combat troops on the ground to carry [out] military missions on the ground. We don't need that," the prime minister said in an interview on National Public Radio.
"We can destroy Daesh. I think we have many forces on the ground who are fighting Daesh. We can advance on Daesh. But we need proper intelligence and proper air cover and support," Abadi said, using an Arabic term for the Islamic State militants.
Experts inside and outside the U.S. military say Abadi's reluctance to allow an expanded U.S. presence in the fight reflects the influence of Iran and the Shiite sectarian factions in Baghdad who oppose American influence in Iraq.