In public messages and in recent actions in Syria, the group’s leaders are acknowledging the terrorist organization’s declining fortunes on the battlefield while bracing for the possibility that its remaining strongholds could fall.

At the same time, the group is vowing to press on with its recent campaign of violence, even if the terrorists themselves are driven underground. U.S. counterterrorism experts believe the mass­casualty attacks in Istanbul and Baghdad in the past month were largely a response to military reversals in Iraq and Syria.

Such terrorist acts are likely to continue and even intensify, at least initially, analysts say, as the group evolves from a quasi-state with territorial holdings to a shadowy and diffuse network with branches and cells on at least three continents.

Indeed, while the loss of a physical sanctuary would constitute a major blow to the Islamic State — severely limiting, for example, its ability to raise money, train recruits or plan complex terrorist operations — the group’s highly decentralized nature ensures that it will remain dangerous for some time to come, according to current and former U.S. officials and terrorism experts.