BRUSSELS — When Defense Secretary Ashton B. Carter convenes a meeting here on Thursday to cajole about two dozen of his counterparts into contributing more to the American-led campaign against the Islamic State, he will face one of his biggest leadership tests since he took office a year ago.
President Obama told Mr. Carter in December that as the administration intensifies its efforts against the Islamic State, other countries — particularly Arab ones — need to do more. Mr. Carter said Tuesday that he was confident he would leave the meeting this week with pledges of aid like air support, special forces, trainers and money.
But foreign policy analysts and former American diplomats say that while the administration may gain some help from European allies, it continues to miscalculate what the Arab countries are willing to do.
“The thing is, the Islamic State is nobody’s top enemy,” said Ryan C. Crocker, a former United States ambassador to Iraq. “For the Turks, the enemy is the Kurds, and for the Sunni Arabs, it’s Iran, followed by Assad,” he added, referring to President Bashar al-Assad of Syria.
While the administration wants to avoid the appearance that the United States is “going it alone” again in the Middle East, other countries understand that the American military will continue its campaign regardless of whether they provide any help. Mr. Carter acknowledged on Tuesday that Mr. Obama had not set any threshold for contributions that would be needed for the United States to maintain the effort against the Islamic State, also known as ISIS or ISIL.
William McCants, the author of “The ISIS Apocalypse,” said that Mr. Carter had expressed an understandable frustration about “our allies’ free-riding.” But, Mr. McCants added, “I don’t see how he brings them along without a major realignment of Obama policy, and I don’t see that coming.”
Mr. Obama wants to enlist more help so that he will not need to send more ground forces into the region. Though the president campaigned in 2008 on pulling military forces out of Iraq, the United States has about 3,700 troops there, counting a handful of Special Operations forces on the ground in Syria. The campaign has proceeded in fits and starts, and the American public remains skeptical that the United States has a plan to defeat the Islamic State.
Since taking office in February 2015, Mr. Carter has kept a fairly low profile. Secretary of State John Kerry often takes the lead in speaking publicly about foreign affairs. And, unlike Mr. Kerry, Mr. Carter was not at the table for the administration’s most significant achievement in the Middle East: the agreement with Iran to limit its nuclear program.
But he has played a direct role in trying to expand the military coalition against the Islamic State, work that until this week had largely gone on behind the scenes.
In closed-door meetings, phone calls and detailed letters, he has explained to foreign leaders the wide range of ways they can help, from providing troops to helping with reconstruction. “If you don’t have a lot of capability but you want to make a contribution, you can literally do that, make a contribution,” Mr. Carter said in a briefing with reporters on a flight to Brussels from Washington on Tuesday.
There have been mixed signs in recent weeks about how willing other nations are to help. The Dutch have said they will join the air campaign, while the Canadians said they would stop participating in airstrikes but would increase their training of ground forces. Peter Cook, a Pentagon spokesman, said Monday that Mr. Carter appreciated the decision “to step up Canada’s role in the campaign at this critical time.”
Saudi Arabia and the United Arab Emirates have sought to give the appearance that they are doing more. Last week, they offered to send ground troops to Syria to fight the Islamic State.
But that offer came with many caveats, as outlined in a news conference in Abu Dhabi on Sunday by the Emiratis’ minister of state for foreign affairs, Anwar Gargash. “We are not talking about thousands of troops,” he said. He added that “U.S. leadership on this” would be a prerequisite.
In an interview, Landon Shroder, an intelligence analyst for corporations in Iraq, translated that statement about American leadership to mean “total and absolute United States domination” of a ground effort in Syria, with thousands of American ground troops. Mr. Obama has said he has no intention of making such a commitment.
The United States’ Sunni Arab allies in the region provided some military support when the campaign began in 2014, but they have largely withdrawn from the fight. The Persian Gulf countries, led by Saudi Arabia, are still angry at the United States over the nuclear pact with Iran, and they fret that the Obama administration has moved closer to Tehran, despite administration assurances to the contrary.
What is more, the Sunni Arabs are far more interested in getting rid of Mr. Assad than they are of getting rid of the Islamic State. As long as the administration continues to not make a priority of deposing Mr. Assad, Saudi Arabia and the other Sunni Persian Gulf countries will remain lukewarm in the battle against the Islamic State, regional experts say.
The Saudi-led war against Iranian-backed Houthis in Yemen has drained most of the Gulf Arabs’ fighting capacity, international experts say. And that military effort is against an adversary — Iran — that dominates the psyche of the Gulf Arab countries far more than the Islamic State.
Mr. Carter said on Tuesday that “America is willing and determined to lead, to devise the campaign plan and add its own major contributions.”
“But we’re looking for others to make a contribution as well,” he added. “And their attendance at this meeting suggests a willingness on the part of almost all of them to do more.”