Iraqi Defense Minister Khaled al-Obeidi, right, speaks during a news conference with U.S. Army General Martin Dempsey in Baghdad on March 9. (Ahmed Saad/Reuters)

The top U.S. military officer urged Iraqi leaders Monday to take steps to ensure the effectiveness of U.S. and allied security aid, calling for additional reforms to military leadership and pay systems and increased recruitment of troops to fight the Islamic State.

Gen. Martin Dempsey, chairman of the Joint Chiefs of Staff, also raised concerns about the Shiite-led government’s record so far in securing buy-in from the country’s Sunni Arabs.

“I wanted them to know we are eager for them to keep all the lines of effort, to include the governance line, making progress,” he told reporters after meeting with Iraqi Prime Minister Haider al-Abadi and Defense Minister Khaled al-Obeidi during a day-long visit.

Dempsey said that seven months of airstrikes by the U.S.-led coalition were achieving results against the Islamic State, which is scrambling to defend multiple fronts.

During his visit, Dempsey heard the Iraqis express support for another of their military backers: Iran. Tehran’s increasingly overt role in supporting Shiite militias in Iraq has created more than a little anxiety in Washington.

Dempsey raised concerns about relations between Sunnis and Shiites in Iraq. (Sabah Arar/AFP/Getty Images)

Speaking alongside Dempsey at a news conference, Obeidi praised the contribution of Iranian-backed “popular mobilization” paramilitary fighters, who make up the bulk of a force attempting to retake the city of Tikrit from Islamic State militants.

Iraq has “asked for help from many countries that we have a strategic relationship with, and that includes the United States, of course, and also Iran,” Obeidi said.

“We are in a state of war, and we look to our friends to help us in this confrontation,” he said. “The situation is acceptable to us.” So far, equipment, training and other types of support from Iran’s military have enhanced the fighting power of the organized militias and volunteer fighters in Iraq. Dempsey has focused his concern on the aftermath of the current battles, saying that Iran must prove that its support extends to helping Iraq build a stable, unified country.

While the Obama administration is in talks to end Iran’s nuclear program, Washington and Tehran remain on opposite sides of a range of issues, including the conflict in Syria.

Dempsey, who spent three years in Iraq during the war that began in 2003, said the long-term viability of the international coalition fighting the Islamic State could be threatened if Iraq does not draw in Sunnis. He said some Sunni Arab nations in the alliance have raised concerns to him that Abadi’s government is not doing enough to help Iraq’s Sunnis.

The Sunni extremists of the Islamic State, a radical al-Qaeda offshoot also known as ISIS or ISIL, pose a threat not just in Iraq and Syria but across the region and potentially in the West.

While Abadi has committed to increasing Iraqi Sunnis’ participation in the government and armed forces, progress has been slow. Efforts to build Sunni local forces to balance the Shiite militias have moved haltingly, while a proposal to create a multisectarian national guard has not passed the Iraqi parliament. When Abadi took over as prime minister last year, he promised to reach out to all of Iraq’s sects and ethnicities.

“I come away a bit concerned that it’s going to be difficult to sustain the coalition for the rest of the challenge, which is trans-regional, unless the government of Iraq can actually form that national unity platform,” Dempsey said.

In the near term, Dempsey said that U.S. and allied efforts to help Iraq’s armed forces could be hindered by weak leadership in the Iraqi military, especially at the brigade level, as well as by failures to pay and equip soldiers, and recruit people for new training programs.

“They’ve got to deliver the clay, and we’ll mold it,” he said. Iraqi leaders agreed to work on those problems.

The Army general said the U.S.-led coalition would consider using air power to defend historic monuments under threat from the Islamic State, as Iraqi officials have urged.

But Dempsey cautioned that any such request would have to be weighed against other priorities, such as protecting civilians and key infrastructure or the capital, Baghdad.

“We will consider it, but it has to fit into the priority of all the other things we’re being asked to do on behalf of Iraq,” he said.