U.S. and coalition forces have started to train Iraqi soldiers at four sites across the country even as more American troops prepare to deploy to join the growing fight against the Islamic State extremist group, a top general said Tuesday.

"There's still a big fight going on here, so we're trying to get the Iraqi army ready to get back on the offensive," said Maj. Gen. Paul Funk, commander of Coalition Joint Forces Land Component Command-Iraq and the 1st Infantry Division. "They've blunted Daesh, and Daesh is losing across the country. We're trying to build that fist so they can finish the fight against Daesh in Iraq."

Funk, who is in charge of U.S. and coalition land forces in Iraq, refers to the Islamic State as Daesh, an Arabic term that leaders of the extremist group reportedly hate and consider pejorative. It's a term many leaders, including Lt. Gen. James Terry, commander of the U.S. war effort in Iraq and Syria, use as well.

There are about 1,600 U.S. troops in Iraq, with an additional 1,300 on the way. About 1,000 of the deploying troops are from the 82nd Airborne Division's 3rd Brigade Combat Team, and they are part of a 1,500-troop increase authorized in November by President Obama.

The additional troops should flow into Iraq between mid-January and March, Funk said during a phone interview from Baghdad.

Another 250 paratroopers, also from 3rd BCT, 82nd Airborne Division, are deploying to replace troops already in theater.

As the troops deploy, the U.S. has put in place a "bridging solution" so that the Iraqis' training can begin earlier, Funk said. This includes temporarily using troops from the 1st Infantry Division and the Special Purpose Marine Air-Ground Task Force who are already in the Central Command area of operations to stand up four Building Partner Capacity sites, which are part of the White House's strategy, to train the Iraqis.

"The uniform of the American soldier and Marine means two things across the globe," Funk said. "It strikes fear in the hearts of our enemies, and it strikes hope in our friends. That kind of helps bolster the Iraqi army, which is what we want it to do."

The four training locations are in al-Asad in Anbar province, Erbil in the north, and Taji and Besmayah in the Baghdad area. More sites are expected to be stood up, but it's too soon to say how many there will be or where they'll be located, Funk said.

For now, "our job is to make sure [the four sites] run smoothly," he said. "We're training their forces on move, shoot and communicate, medical, maintenance, how to use direct and indirect fires, and we're really focused on training the trainers, training the Iraqi army to build some depth in their training program. That's the piece that builds some longevity and adaptability."

The intent is to grow strong Iraqi noncommissioned officers and officers who can then, in turn, train their junior soldiers, Funk said.

"Our mission is to advise and assist the Iraqi army and to build partner capacity," he said. "By that it means we'll set up a training program for the Iraqi forces, and it also involves advising them on combat operations."

It's too early to say which specific areas the Iraqis will need more training, Funk said.

"This is the first week," he said. "We're doing assessments for the first three weeks, then we'll adapt the program."

Priorities for now include urban combat techniques and the ability to move, shoot and communicate at the battalion level, Funk said. These priorities are in line with what Iraqi leaders are seeking, he said.

"They want to get better at urban operations, they want to get better at fires and maneuver, and they want to understand air-ground integration," Funk said. "That's what they're asking for at the battalion and brigade levels."

At the division level, Iraqi leaders are looking for guidance on how to sustain logistics over long distances and how to structure the army, Funk said.

"That's the kind of things they're after," he said. "Also, more airstrikes. They like to kill Daesh. We're together on that."

The Iraqis have already had success against the Islamic State, Funk said.

"Last week, in Erbil, they took back over 2,500 kilometers of terrain," he said. "Just last month, the Iraqi army took back Bayji and all the ground between here and Bayji, that's 600 kilometers of terrain. Even in Anbar, they continue to blunt everything Daesh tries to do. I think the Iraqis have blunted the advance of Daesh, and they're getting the conditions set to conduct an offensive to drive Daesh out."

Also growing is the international coalition that's coming together to fight the Islamic State, Funk said. So far, more than 20 nations are contributing to ground operations.

"There's a great coalition here that's working together very well to bring these Building Partner Capacity sites to life," he said. "That's the encouraging thing. The entire international community is fighting Daesh. It's not just a U.S. Army or U.S. Marine fight. It's a coalition."

The U.S. and its partners are in the fight for the long-haul, Funk said.

"I think the estimates range from three years to who knows how long, but it really becomes event-based," he said. "If the tribes come to the fight, it could go faster. If they don't, it could take longer. It's really hard to tell, as we're in the nascent stages of this thing, but it depends on the assessment of the training piece. [The Iraqis] are engaged, and they want to learn."

Funk said he's confident in the Iraqi forces.

"The Iraqis can do this mission," he said. "What we have now is probably the new patriots of Iraq. These guys are coming into the army, they know they're in the fight."

As for him, Funk said being back in Iraq has been "surreal."

"You're talking to an old Iraq vet," said the two-time veteran of Operation Iraqi Freedom and veteran of Operation Desert Shield/Desert Storm. "It's surreal to fly into Baghdad and see all the lights. There's normal life going on, there's electricity all the way up to Erbil, traffic's flowing normally. It was something to see. While they still have problems, it was something to see that they're trying to get on with life, at least in Baghdad."