The 7,000 Iraqi army troops who have recently completed American-led training programs are not involved in the massive counteroffensive that Iraq launched this week against Islamic State militants in Anbar province, U.S. and coalition officials said.

Instead, the Iraqi campaign will involve several thousand fighters from the Iraqi army as well as some Shiite militias and Sunni tribal forces now under command and control of the Iraqi government in Baghdad. The Iraqis launched the new campaign just days after abandoning Ramadi in a humiliating defeat May 17.

A spokesman for the American-led coalition declined to identify the deployment locations of the Iraqi troops who have received training from the U.S. coalition, citing operational security concerns.

The spokesman, Jens Lunde, said those troops have participated previously in operations in Karma, al Bagdadi and northern Baghdad and also supported protection for Shiite pilgrims going to a revered mosque in Kadhimiya, a suburb of Baghdad.

U.S. defense officials note that the American-led mission is limited to training, and follow-on personnel decisions about where to deploy those troops rest with the Iraqi government.

Some experts say Iraqi leaders are making a strategic decision in holding back their troops who were trained by Americans and may be more skilled than other rank-and-file Iraqi troops.

The fight against Islamic State militants in Ramadi could be a costly battle of attrition during its initial phase, similar to the fight in Tikrit in March, said Ramzy Mardini, a former State Department official who is a nonresident fellow with the Atlantic Council.

"If there's little confidence that Ramadi will be a quick and decisive victory, then there's little incentive to be the ones on the front lines," Mardini said.

"There is also the reality that the Iraqi security forces, and especially the weak prime minister, cannot politically afford another humiliating defeat. So this is a way to perhaps hedge their bets. If ISIS is victorious, the blame will be placed elsewhere. If it appears ISIS is going to lose, then I imagine there's a growing likelihood the recent U.S.-trained forces will be deployed."

The Islamic State's seizure of Ramadi prompted the U.S. to fast-track a shipment of 2,000 AT4 anti-tank weapons to the Iraqi army. Those weapons are intended to counter the Islamic State's increasingly effective use of vehicle-born improvised explosive devices.

In Ramadi, some of those VBIEDs were built using armored, American-made Humvees, causing catastrophic damage and playing a key role in the militants' victory over the Iraqi forces, according to U.S. officials.

The AT4 anti-tank weapons will be delivered in June, defense officials said.

Defense Secretary Ash Carter recently ruffled feathers in Baghdad by suggesting that the Iraqi defeat in Ramadi raised questions about their "will to fight."

Speaking on CNN on Sunday, Carter said: "What apparently happened was that the Iraqi forces just showed no will to fight. They were not outnumbered but in fact they vastly outnumbered the opposing force, and yet they failed to fight."

On Wednesday, on a flight to Asia, Carter told reporters that top U.S. officials are working to identify ways to make the current train-and-equip effort in Iraq more effective.

"One of the last things I did before I left Washington was meet with my team and ask them ... what can we do to enhance the effect of the train-and-equip" mission, Carter told reporters.

"I think training and equipment affect the effectiveness of the forces and therefore their ability to operate, their confidence, and their ability to operate. So there's a direct relationship."