American officials acknowledge that they face a daunting task in gathering, analyzing and disseminating to Iraqi and Western intelligence services a collection of information from Mosul that is expected to dwarf the 20 terabytes of data retrieved so far in Manbij. One terabyte is equal to the contents of a million books.

The Pentagon’s Joint Staff and the Defense Intelligence Agency have been providing intelligence support to the Iraqis for the past two years, American officials said, but there has not yet been a fight to match the size and scope of the battle to retake Mosul, where half of the city’s previous population of two million still resides.

The American-led coalition must be able to offer intelligence support in the Mosul operation to more partner forces — including the Iraqi Army, counterterrorism service and police, as well as Kurdish pesh merga fighters — than in any previous operations to retake other cities.

As a result, in the military’s most recent deployment of more than 600 additional troops, dozens of military and civilian intelligence analysts were dispatched to several locations around Iraq. Most were in place just before the Mosul offensive began, but some are still trickling in.

“Whenever you liberate a city the size of Mosul, you can expect to get a tremendous amount of information,” said Col. John L. Dorrian, the chief American military spokesman in Baghdad. “Certainly, if we have a window of opportunity that presents itself rather quickly, we do have adequate forces in theater to go ahead and act upon that.”

The intelligence surge would most likely “give us a lot of insight into Daesh networks not just in Iraq and Syria, but it also gives insight into how they export terror around the world, some of the people they work with, how they finance themselves,” Colonel Dorrian said.

That is important because even as the Islamic State loses its physical caliphate, or religious state, in Iraq and Syria, the group can still inflict deadly assaults, senior American counterterrorism officials say. “It’s our judgment that ISIL’s capacity and ability today to carry out attacks in Syria and Iraq and abroad has not thus far been significantly diminished,” Nicholas J. Rasmussen, the director of the National Counterterrorism Center, told Congress last month. “The tempo of ISIL-linked terrorist attacks and terrorist activity in Europe and other places around the globe is a reminder of that global reach.”

“This external operations capability has been building and entrenching over the past two years,” he warned, “and we don’t think that battlefield or territorial losses alone will be sufficient to completely degrade the group’s terrorism capabilities.”