WASHINGTON — The Islamic State is expanding beyond its base in Syria and Iraq to establish militant affiliates in Afghanistan, Algeria, Egypt and Libya, American intelligence officials assert, raising the prospect of a new global war on terror. 

Intelligence officials estimate that the group’s fighters number 20,000 to 31,500 in Syria and Iraq. There are less formal pledges of support from “probably at least a couple hundred extremists” in countries such as Jordan, Lebanon, Saudi Arabia, Tunisia and Yemen, according to an American counterterrorism official who spoke on the condition of anonymity to discuss confidential information about the group.

Lt. Gen. Vincent R. Stewart, the director of the Defense Intelligence Agency, said in an assessment this month that the Islamic State, also known as ISIS or ISIL, was “beginning to assemble a growing international footprint.” Nicholas Rasmussen, the director of the National Counterterrorism Center, echoed General Stewart’s analysis in testimony before Congress last week. 

But it is unclear how effective these affiliates are, or to what extent this is an opportunistic rebranding by some jihadist upstarts hoping to draft new members by playing off the notoriety of the Islamic State.

Abu Bakr al-Baghdadi, the leader of the Islamic State, to which a broad array of fighters are swearing allegiance.

ASSOCIATED PRESS

Critics fear such assessments will once again enmesh the United States in a protracted, hydra-headed conflict as President Obama appeals to Congressfor new war powers to fight the Islamic State. “I’m loath to write another blank check justifying the use of American troops just about anywhere,” said Representative Adam B. Schiff of California, the senior Democrat on the House Intelligence Committee. 

The sudden proliferation of Islamic State affiliates and loyalist fighters motivated the White House’s push to give Mr. Obama and his successor new authority to pursue the group wherever its followers emerge — just as he and President George W. Bush hunted Qaeda franchises outside the group’s headquarters, first in Afghanistan and then in Pakistan, for the past decade. 

“We don’t want anybody in ISIL to be left with the impression that if they move to some neighboring country, that they will be essentially in a safe haven and not within the range of United States capability,” Josh Earnest, the White House press secretary, said on Wednesday.

The Islamic State began attracting pledges of allegiance from groups and individual fighters after it declared the formation of a caliphate, or religious state, in June 2014. Counterterrorism analysts say it is using Al Qaeda’s franchise structure to expand its geographic reach, but without Al Qaeda’s rigorous, multiyear application process. This could allow its franchises to grow faster, easier and farther.

The aftermath of a Jan. 29 attack in the Sinai Peninsula by an Egyptian group rebranded as a “province” of the Islamic State.
ALAA ELKAMHAWI / ALMASRY ALYOUM, VIA EUROPEAN PRESSPHOTO AGENCY

“Factions which were at one time part of Al Qaeda and its affiliates, as well as groups loyal to it or in some ways working in tandem with it, have moved on to what they see as more of a winning group,” said Steven Stalinsky, executive director of the Middle East Media Research Institute in Washington, which monitors Arabic-language news media and websites.

The Islamic State’s attraction, even in the West, was proved when Amedy Coulibaly, one of the gunmen in the Paris terrorist attacks last month, declared allegiance to the group.

In Afghanistan last week, an American drone strike killed a former Taliban commander, Mullah Abdul Rauf Khadim, who had pledged allegiance to the Islamic State and had recently begun recruiting fighters. But that pledge seemed to indicate less a major expansion of the Islamic State than a deepening of internal divisions in the Taliban.

There is no indication that the Islamic State controls territory in Afghanistan, but it has signaled its interest in Afghanistan and Pakistan, and has reportedly sent envoys there to recruit.

Similarly, until recently, leaders of Al Qaeda in the Arabian Peninsula, in Yemen, used nonconfrontational language to mask simmering disagreements with the Islamic State and its head, Abu Bakr al-Baghdadi. But tensions peaked in November, when a faction of Qaeda fighters there swore loyalty to Mr. Baghdadi. 

Any authorization to use American military force against the Islamic State could arguably also cover interventions in Egypt and Libya, where active militant organizations have pledged allegiance to the group and have received its public acknowledgment as “provinces” of the putative caliphate.

Although there is little or no public evidence that the Islamic State’s leaders in Syria and Iraq have practical control over its North African provinces, its influence is already apparent in their operations and is destabilizing the countries around them. A publication released by the central group last week included a photograph of fighters in Libya with its affiliate there parading 20 Egyptian Christian captives in the Islamic State’s trademark orange jumpsuits, indicating at least a degree of communication.

In Egypt, the Sinai-based extremist group Ansar Beit al-Maqdis sent emissaries to the Islamic State in Syria last year to seek financial support, weapons and tactical advice, as well as the publicity and recruiting advantages that might come with the Islamic State name, according to Western officials briefed on classified intelligence reports.

Ansar Beit al-Maqdis began adopting the Islamic State’s signature medieval punishment, beheadings, even before a formal merger. After becoming the Sinai Province of the Islamic State in November, the group’s online videos and statements claiming responsibility for attacks began to take on more of the sophistication and gore associated with its new parent group. 

Unlike the Islamic State fighters in Syria and Iraq, the Sinai Province has so far focused on hitting the security forces of the military-backed Egyptian government, largely avoiding attacks on Westerners, members of Egypt’s Christian minority or other purely civilian targets.

But despite the government’s escalating crackdown in Egypt, the militants appear to have grown bolder and more advanced since linking themselves to the Islamic State. On the night of Jan. 29, for example, the Sinai Province claimed responsibility for a series of coordinated bombings that targeted security forces across the region, killing 24 soldiers, six police officers and 14 civilians, according to the Egyptian state news media. 

In neighboring Libya, at least three distinct groups have declared their affiliation with the Islamic State, one in each of the country’s component regions: Barqa in the east, Fezzan in the desert south, and Tripolitania in the west, around the capital. With fighting among other regional and ideological militias having already plunged the country into chaos, the Islamic State affiliates pose a new obstacle to Western attempts to negotiate a truce or a unity government.

Western officials, especially in southern Europe, fear that the three Libyan “provinces” could evolve into bases for Islamic State fighters traveling across the Mediterranean, into Egypt or elsewhere in North Africa. Eastern Libya has already become a training ground for jihadists going to Syria or Iraq and a haven for Egyptian fighters staging attacks in the neighboring desert.

Ambassador Deborah K. Jones, the American envoy to Libya, posed a question on Twitter in a plea for unity this month: “Can a divided #Libya withstand #ISIL/Daesh?” she wrote, using the English and Arabic shorthand for the Islamic State.

The Islamic State’s self-proclaimed provinces have compounded Libya’s instability by introducing the prospect of Islamist-against-Islamist violence between those who support and those who oppose the group. But Tripolitania has leapt to the fore as the province that most clearly threatens Westerners and Western interests. 

Last month, fighters under the group’s banner claimed responsibility for a brazen attack on a luxury hotel in the capital, Tripoli, that is a hub for visiting Westerners and leaders of the Islamist-backed provisional government.

At least eight were killed, including David Berry, an American security contractor who had served as a Marine. Two of the Islamic State fighters died in a battle against government forces, a sign of the Islamist-versus-Islamist volatility the group had injected into the Libyan chaos.

“It is a real conflict,” said Frederic Wehrey, a senior policy analyst at the Carnegie Endowment for International Peace who recently visited Libya. 

“The Islamic State guys are trying to carve out territory” apart from the broader Islamist coalition and are “challenging them on their own turf,” he said, while other extremists are “peeling off, gravitating to the Islamic State and becoming bolder.”

Eric Schmitt reported from Washington, and David D. Kirkpatrick from Cairo. Rukmini Callimachi contributed reporting from New York, and Ben Hubbard from Riyadh, Saudi Arabia.