The Pentagon said Friday it was moving to increase the number of American troops in Iraq amid new strikes this week that killed the Islamic State’s finance minister and other senior leaders. Still, top U.S. defense officials say the deaths won’t “break the back” of the extremist group, which is in a fierce fight for an ancient city in Syria and claimed responsibility for bombing a soccer stadium in Iraq.

Defense Secretary Ash Carter said the U.S. progress in eliminating members of the IS “cabinet” was hampering its ability to conduct and inspire attacks against the West. The announcement came as the battle to retake the Syrian city of Palmyra entered its third day and Iraqi forces continued their march to recapture Mosul. A suicide bombing in a soccer stadium south of Baghdad, killing nearly 30 people, underscored the difficult fight ahead.

Gen. Joseph Dunford, chairman of the Joint Chiefs of Staff, told Pentagon reporters that recommendations on ways to increase U.S. support for Iraq’s ground fight against IS will be discussed with President Barack Obama soon.

“The secretary and I both believe that there will be an increase in U.S. forces in Iraq in coming weeks, but that decision hasn’t been made,” Dunford said. He did not say how big that increase might be.

He and Carter said accelerating the campaign against the Islamic State will include more assistance like the artillery fire and targeting help that U.S. Marines provided earlier this week to Iraqi forces advancing on Mosul. But they said American forces remain well behind the front lines.

“I think there’s a lot of reasons for us to be optimistic about the next several months,” Dunford said. “But by no means would I say that we’re about to break the back of ISIL or that the fight is over.”

Using an acronym for the militant group, Carter said the U.S. is “systematically eliminating ISIL’s cabinet,” killing several key members in strikes this week.

Carter would not provide details about the strikes, but a senior U.S. official said the group’s financial minister was killed along with two associates in a U.S. raid in Syria. The official was not authorized to discuss the operations so spoke on condition of anonymity.

Carter said the finance minister, who is known by several names, including Abdul-Rahman Mustafa al-Qaduli and Haji Imam, was a “well-known terrorist” who had a hand in terrorist plots outside of Iraq and Syria.

He said al-Qaduli has been associated with IS dating back to its earliest iteration as al-Qaida in Iraq. He said he had worked under Abu Musab al-Zarqawi as a liaison for operations in Pakistan and was “responsible for some external affairs and plots.” Carter said he was not aware of any link between al-Qaduli and this week’s terrorist attacks in Brussels.

In a separate operation, a U.S. airstrike in Mosul killed another top IS leader, the official said. Carter identified the man as Abu Sarah and said he was one of the leaders charged with paying militant fighters in northern Iraq.

The successful attacks are part of a string of recent strikes targeting the leadership of the group, which has lost territory in both Iraq and Syria. Earlier this month the Pentagon said it killed Omar al-Shishani, described as the Islamic State’s “minister of war,” in an airstrike in Syria. In November, the Pentagon said an airstrike in Libya killed Abu Nabil, another top IS leader.

Earlier this week, U.S. military officials confirmed the creation of a Marine outpost, dubbed Fire Base Bell, in Iraq. U.S. Marines operating from the small base provided targeting assistance and artillery fire to support Iraqi troops retaking several villages in the initial stages of their march to Mosul. It’s the first such base established by the U.S. since it returned forces to Iraq in 2014.

Carter has also said the U.S. is looking at a number of options to “accelerate” the fight against IS. Those options have not yet officially been submitted to the White House for approval. They could include sending additional U.S. forces to Iraq, using Apache helicopters for combat missions, deploying more U.S. special operations forces or using American military advisers in Iraqi units closer to the front lines.

In Iraq on Friday, IS claimed responsibility after a suicide bomber blew himself up during a match in the small soccer stadium in the city of Iskanderiyah, 30 miles from Baghdad. The attack killed at least 29 people and wounded 60, security officials said.

In Syria, government forces recaptured a Mamluk-era citadel in Palmyra from IS, Syrian state media and monitoring groups said. Syrian and Russian warplanes struck at least 56 targets inside IS-held areas of the city and pro-government militias supported the army’s advance, according to the Syrian Observatory for Human Rights, a Britain-based monitoring group.

Palmyra has been controlled by the extremist group since May, and the militants have destroyed some of its best known Roman-era archaeological relics. Recapturing it would be a significant victory for Syrian government troops, who have been supported by Russian airstrikes in their advances.

Government forces also cut the road between Palmyra and another IS bastion, the town of Qaryatayn, weakening the group’s hold over its two central Syrian outposts.

(AP)