WASHINGTON — As Iraqi forces launch their long-awaited campaign to retake the city of Mosul from the Islamic State, President Obama’s doctrine of aiding other countries militarily rather than leading every fight is facing its greatest test yet.
How well the Mosul campaign goes, not just the fighting over the coming days and weeks but the rebuilding of the city in the months after that, will help define Mr. Obama’s legacy as a wartime leader who sought to take the United States off the front lines of the counterterrorism war.
On Monday, in keeping with the president’s insistence that the Iraqis take the lead, the White House said that Prime Minister Haider al-Abadi was “calling the shots.” But the reality is that roughly half of the 5,000 American troops now in Iraq are likely to be involved in the operation, which could eventually require 30,000 Iraqi and Kurdish troops.
The podcast that makes sense of the most delirious stretch of the 2016 campaign.
About 200 to 300 of the Americans are Special Operations commandos advising Iraqi and Kurdish troops — a mission that will put them a few miles behind the front lines, communicating with Iraqi soldiers via radio. A few dozen are forward air controllers, who are already calling in airstrikes against Islamic State targets, Lt. Gen. Stephen Townsend, the American commander in charge of the coalition in Iraq and Syria, said on Monday.
The other Americans range from Apache helicopter pilots to intelligence analysts at Iraq’s military headquarters.
“Our men and women in uniform, who are serving in Iraq, are putting themselves in harm’s way,” said the White House press secretary, Josh Earnest. “There’s no one, including the commander in chief, who would downplay the risks that they are taking on our behalf.”
For the White House, there were other tensions, including the need both here and in Iraq to cast the United States in a supporting rather than a central role. At one point, Mr. Earnest noted that the United States had helped the Iraqis stabilize two other smaller Iraqi cities, Ramadi and Tikrit.
“We’ve done this,” Mr. Earnest said, before catching himself. “I should say, the Iraqis have done this — on a smaller scale.”
Mosul is the largest example of a counterterrorism model that the Obama administration has put in place from Afghanistan to Libya. In Somalia, Special Forces troops are training Somali and African troops to combat the militants of the Shabab. In Syria, about 300 Special Forces troops are aiding Syrian Kurdish and Arab militias with training and air support in the battle against the Islamic State.
“We need partners to fight terrorists alongside us,” Mr. Obama said at West Point in 2014, when he laid out the counterterrorism strategy to cadets graduating from the United States Military Academy.
But these partnerships have a mixed record. In Iraq, troops have successfully driven the Islamic State out of every major city except Mosul. But in Afghanistan, the Taliban have made steady gains in seizing territory from the American-trained Afghan security forces. They now control at least 30 percent of Afghanistan, and threaten the northern city of Kunduz.
The United States has already failed once in training Iraqi troops. After $25 billion in aid and nearly a decade of training, the Iraqis melted before the advancing militants of the Islamic State in 2014.
Critics have derided Mr. Obama’s approach as an example of “leading from behind.” But other officials said that if the Mosul operation were successful, it would vindicate Mr. Obama.
“The bottom line is the result,” said Philip H. Gordon, a former coordinator of Middle East policy in the National Security Council. “When he leaves office, is ISIS failing? Is it defeated, if not destroyed? That more than anything will determine how the strategy is ultimately judged.’’
“There is a decent chance that judgment will be positive,” he added.
First, however, the Iraqis have to take Mosul, a campaign the White House acknowledged would be protracted and difficult, and might not be completed by the time Mr. Obama leaves office in January. As recently as Sunday, the objectives of American airstrikes included a range of Islamic State targets near the city, including tunnels, weapon caches, mortars and vehicles, according to the military command in Baghdad.
Peter Cook, the Pentagon press secretary, said it was too soon to tell whether American forces would accompany Iraqi and Kurdish troops into Mosul itself. “There are Americans on the outskirts of the city,” Mr. Cook told reporters, saying they were currently behind the front lines.
Leading up to this latest phase of the campaign, Apache attack helicopters equipped with Hellfire missiles have been striking targets in northern Iraq. They were not used in the early hours of Monday’s battle, the Pentagon said. American pilots are also flying surveillance missions and operating armed drones in the combat zone, officials said.
American commanders have warned that Iraqi and Kurdish forces will face a city laced with explosive booby traps, oil-filled trenches and underground tunnels to allow Islamic State fighters to pop up and carry out guerrilla-style attacks against the government forces.
Some Islamic State combatants, including foreign fighters, are expected to fight to the death. But others are likely to fall back and try to slip away to the west and the Syrian border.
After weeks or months of fierce urban combat, a critical question for the Iraqi government and the Obama administration is who will secure and eventually govern the city once the Islamic State is driven out.
The Kurds have assured American officials that they will not send their forces into Mosul once it has been secured. Nor does the United States want Iraq to keep its largely Shiite army inside the predominantly Sunni city any longer than it needs to.
Iranian-backed Shiite militias, which are a politically powerful movement in Iraq, have been accused of detaining and killing hundreds of men who fled the fighting in and around Falluja this year.
Thus, American officials said, security will largely rest in the hands of newly trained local police officials. More than 20,000 Sunni tribal fighters, whom the Iraqis and Kurds are vetting, will also help with security. While this plan puts local security forces in the lead, it also means that one of the most complicated and high-risk phases of the overall operation will be entrusted to lightly armed fighters whom the United State does not directly advise.
Another big worry for administration officials is the lack of a detailed plan to govern Mosul, Iraq’s second-largest city, which had two million residents before the Islamic State’s takeover in 2014.
Outside the city, competing groups of Kurds, Shiites and others are already counting their political spoils, raising fears that retaking the city could aggravate tensions between Sunnis in Mosul and the Shiite-dominated government in Baghdad that fueled the Islamic State’s rise in the first place.
While some Pentagon aides pressed for more definitive plans, other administration officials say that American diplomats will help broker political power-sharing arrangements between Iraqis, Kurds and various other groups in Nineveh as the campaign unfolds.
“Everyone will want a piece of the pie,” said Matthew Henman, managing editor of IHS Jane’s Terrorism and Insurgency Center in London. “A lot of actors want to be calling the shots.”