Iraqi troops closing in on Ramadi outnumber Islamic State militants by as many as 10 to one, a U.S. official told Military Times on Friday.

The offensive to wrest back control of the city involves between 8,000 and 10,000 Iraqi security forces, said Army Col. Steve Warren, a spokesman for the U.S.-led coalition overseeing the fight against the Islamic State groupas the group is also known.

No American military personnel are on the ground fighting alongside them, he said.

Three U.S.-trained Iraqi brigades are participating in the operation, Warren said. They face between 600 and 1,000 well-entrenched Islamic State fighters.

American and coalition warplanes have conducted airstrikes in and around Ramadi since the summer, aiming to weaken the militants' grip ahead of the highly anticipated ground operation that began Wednesday.

"We believe the Iraqis will finish soon," Warren said, adding that Iraq's government has a "detailed plan to use tribal fighters, federal police and local police for stabilization" once the city is cleared.

Ramadi, the capital of Iraq's Anbar province, fell in mid-May when thinly supported Iraqi soldiers abandoned their posts ahead of the Islamic State group's advance. Iraq's government said in July it was developing plans to retake the city.

News of the city's fall angered many American veterans who fought in Ramadi during the U.S. military's eight-year occupation of Iraq. More than 70 U.S. troops died as a result of the fighting there during a 2006 campaign to oust insurgents.

On Wednesday, Iraqi soldiers took control of the Palestine bridge northwest of the city, shutting off a key supply route crossing the Euphrates River. As they advanced, American and coalition aircraft took out ISIS snipers and a variety of homemade bombs and heavy weapons.

The air assault continued Thursday with a mix of bombers, fighters, ground-attack jets and drones, U.S. officials said. They hit ISIS command posts and staging areas, destroying buildings, boats and roads in an apparent effort to further eliminate supply lines and cut off escape routes.

About 3,500 U.S. troops are in Iraq, mainly soldiers and Marines tasked with training and advising the Iraqi army. The White House has approved U.S. special operations forces to participate in select surgical missions targeting ISIS fighters in Iraq and Syria, but President Obama has resisted calls to deploy large numbers of American ground troops.

Last month, Army Master Sgt. Joshua L. Wheeler became the first U.S. service member killed by enemy fire while fighting the Islamic State group. He was among several dozen American commandos who helped Kurdish peshmerga fighters conduct a successful hostage rescue at an ISIS prison in Kirkuk province.