Hours before President Obama announced a new U.S. military offensive against the Islamic State, one of his top counter­terrorism officials testified to Congress that the al-Qaeda offshoot had an estimated 10,000 fighters.

The next day a new assessment arrived from the CIA: The terrorist organization’s ranks had more than doubled in recent months, surging to somewhere between 20,000 and 31,500 fighters across Iraq and Syria.

The enormous discrepancy reflects, in part, significant uncertainty among U.S. intelligence agencies over the dimensions of and danger posed by America’s latest Islamist adversary.

But the trajectory of those numbers — and the anxiety that they have induced among U.S. counter­terrorism and military officials — also helps to explain Obama’s decision to go to war against an Islamist group that has yet to be linked to any plot against the United States.

In his speech, Obama laid out a rationale that leaned heavily on what-ifs. The United States has “not yet detected specific plotting against our homeland,” Obama said. But Islamic State leaders “have threatened America and our allies,” he said, and are on a path to deliver on those threats “if left unchecked.”

The White House chief of staff Denis McDonough appears on Sunday political shows and reiterates the president's promise of not using U.S. troops on the ground to fight the Islamic State. (Divya Jeswani Verma/The Washington Post)

The emphasis on hypotheticals was notable for a commander in chief who presided over the creation of a counter­terrorism doctrine in which U.S. strikes are supposed to be contemplated only in cases­ of imminent threat of violent attack. Faced with a terrorist group that is expanding faster than U.S. spy agencies can chart it, the “imminent” threshold appears to have been set aside.

Lisa Monaco, assistant to the president for homeland security and counterterrorism, said in an interview Saturday that the speed at which the Islamic State has grown and amassed re­sources and its efforts to recruit Western fighters have prompted officials to respond differently than they did to terrorist groups elsewhere. “At least at this stage, it’s a really different type of threat that it poses,” she said.

When asked about the revised estimates of Islamic State fighters Friday, White House press secretary Josh Earnest said it indicates “that the group has had some recruitment success after the battlefield ad­vances that they demonstrated back in June, and it reflects some better insight that the intelligence community has been able to gain into the activities” of the Islamic State.

Several factors have fed U.S. anxiety. The Islamic State’s seizure of large chunks of territory in Iraq and Syria has been particularly unnerving to U.S. officials and agencies still haunted by the extent to which a haven in Afghanistan served as an incubator for al-Qaeda and the Sept. 11, 2001, attacks.

U.S. officials have also cited the danger posed by the massive flow of foreign fighters into Syria — including at least 2,000 holding Western passports, enabling them to emerge from the Syrian civil war with Islamist contacts, lethal training and the potential ability to travel throughout Europe and North America unimpeded.

There may also be a significant emotional component. The expanded U.S. strikes were ordered just weeks after most Americans were introduced to the Islamic State on the most brutal terms: through the release of videos in which two U.S. journalists were beheaded by a masked militant speaking with a British accent. Late Saturday, a new video was posted online showing the beheading by Islamic State of British aid worker David Haines, who was abducted in Syria near the Turkish border in March 2013.

Some terrorism experts have questioned Obama’s decision to open a multi­year campaign against the Islamic State — also known as ISIS or ISIL — citing concern that it is being driven more by psychological factors and fear than by evidence that it can significantly harm the United States.

View Graphic U.S. airstrikes in Iraq targeting Islamic State

“The American public has come to equate ad­vances in the Middle East by this one group, ISIS, with the danger of another 9/11,” said Paul Pillar, a former deputy director of the CIA’s Counter­terrorism Center.

Pillar said that the Islamic State is following a playbook that is in many ways the opposite of al-Qaeda’s and that making the group the target of a U.S.-led campaign risks turning its focus toward the United States.

“For them to seize and maintain territory is a major digression from terrorist operations in the West, rather than a facilitation of such operations,” Pillar said.

U.S. strikes can certainly degrade the organization, but “there will be a revenge factor,” he said. “The killing of the two captive journalists was depicted by the group explicitly as retaliation for strikes that had already occurred.”

Attention to that issue and others has been scarce in the limited Washington debate so far over the Islamic State, a debate that has often been dominated by more dire projections.

“There is no contain policy for ISIL,” Secretary of State John F. Kerry said this month. “They’re an ambitious, avowed genocidal, territorial-grabbing, Caliphate-desiring, quasi-state within a regular army. And leaving them in some capacity intact anywhere would leave a cancer in place that will ultimately come back to haunt us.”

Sen. Dianne Feinstein (D-Calif.), the chairman of the Senate Intelligence Committee, wrote in a recent op-ed that “the threat ISIS poses cannot be overstated.” She went on to describe the group as “the most vicious, well-funded and militant terrorist organization we have ever seen.”

Although aspects of Kerry’s and Feinstein’s characterizations are accurate, confusion about the group stems to a large degree from the difficulty in extrapolating its danger to the United States from such adjectives.

The Islamic State emerged from the remnants of an al-Qaeda affiliate in Iraq that was largely dismantled before U.S. forces left the country in 2011. But the organization has taken advantage of the chaos in Syria’s civil war and sectarian tensions in Iraq to regroup.

Beyond its swelling ranks of fighters, the organization has amassed resources at a rapid rate. Its seizure of cities in Iraq this year has enabled it to build an arsenal that includes U.S.-provided weaponry. It also generates an estimated $1 million a day in revenue from black-market oil sales, kidnappings and other criminal enterprises. Matt Olsen, director of the National Counterterrorism Center, said recently that the Islamic State has vastly eclipsed al-Qaeda in its use of the Internet to spread propaganda and entice recruits.

The White House considered that targeting the Islamic State directly could intensify its motivation to strike the United States, Monaco said, which is part of why the president and others have made a point of questioning its religious credentials and overall legitimacy. But she noted that the group has already made clear its intent to target the country.

“We conduct that analysis, but they’ve already shown their brutality,” she said.

The threat the Islamic State poses to the region is in some ways more insidious than direct. Its fighters have swept through Sunni areas of Iraq and Syria where local security forces­ were already weak or disinclined to fight. It would be harder to take on the loyal armies of other countries in the region.

Of greater concern is the flow of foreign fighters, including thousands of Saudis, Jordanians and Tunisians who have probably learned lethal skills in Syria and been drilled in extremist ideology. There have already been demonstrations in support of the Islamic State in Jordan; its flag flutters over some Sunni communities in Lebanon; and Saudi Arabia has conducted sweeps to detain dozens of suspected supporters.

For Saudi Arabia and other gulf nations, there is little incentive to join a military assault on the Islamic State, said Jamal Khashoggi, a prominent Saudi journalist who runs the Al-Arab News Channel. “Nobody wants to be in the middle of a bloody sectarian war,” he said. “And if we go into Syria, do we side with the rebels” or Syrian President Bashar al-Assad?

Similar anxieties have spread across Europe, as thousands of Muslims from France, Germany, Britain and other countries have flocked to the conflict in Syria, a country easier for Western militants to reach than al-Qaeda havens in Yemen or Pakistan.

French authorities earlier this year arrested an Islamic State-linked militant who had returned to that country and was discovered with a stockpile of explosives. Another fighter with ties to the group killed four in an attack on a Jewish museum in Belgium. It is unclear whether either had been acting on direction from the Islamic State.

The number of Western fighters in Syria has dwarfed the migrations to other insurgent hot spots in the past. “No more than 50 to 75 American foreign fighters” made it to Afghanistan between 1986 and 2001, said Evan Kohlmann, a terrorism consultant at Flashpoint Partners. “It’s very difficult for law enforcement to monitor this large a number of people.”

U.S. officials have said that about 100 Americans have either traveled to Syria or attempted to and that perhaps a dozen have linked up with the Islamic State. Moner Mohammad Abusalha — who fought with another extremist group, Jabhat al-Nusra, and was the first known suicide bomber in Syria to come from the United States — recorded a video before his death in May describing how he had eluded FBI surveillance.

The Islamic State’s rivalry with al-Qaeda has emerged as another source of worry for U.S. officials. The group severed ties with al-Qaeda this year, mocking the older network’s leader, Ayman al-Zawahiri, as too timid and declaring itself the founder of a restored Islamic caliphate.

U.S. counter­terrorism officials have warned that a struggle over adherents and resources­ could lead to competition between the two groups. Nicholas Rasmussen, deputy director of the National Counterterrorism Center, warned in a recent briefing for reporters that the “competition for primacy in global jihad” could lead to competition in staging spectacular attacks, compounding the danger to the United States. The rivalry, Rasmussen said, makes each side “more unnerving than it might be if judged purely on its own terms.”

And groups such as al-Qaeda could recruit some of the Islamic State’s most talented foreign fighters, making them better positioned to strike the West, said Frank J. Cilluffo, director of George Washington University’s Homeland Security Policy Institute.

Even so, U.S. officials have drawn significant distinctions between the Islamic State and al-Qaeda affiliates in Yemen and other countries. The Iraq-based group mixes military and terrorist tactics but is not seen as a patient cultivator of elaborate trans­national plots. And there is no indication that its leaders have the technical bomb­making expertise that has enabled al-Qaeda in the Arabian Peninsula to devise devices­ that evaded detection on U.S.-bound aircraft.

“ISIL’s ability to carry out complex, large-scale attacks in the West is currently limited,” Rasmussen said in testimony before a Senate committee last week. The Yemen-based Al-Qaeda in the Arabian Peninsula “remains the al-Qaeda affiliate most likely to attempt trans­national attacks against the United States.”

Liz Sly in Beirut and Julie Tate contributed to this report.