(CNN) -- The Islamic State terror group is now "a credible alternative to al Qaeda" that is "expanding its presence" with foreign fighters returning from Syria, and possibly Iraq, to their home countries, a U.S. intelligence official said Thursday.
The official, who declined to be identified due to the sensitive nature of the information, has direct knowledge of the latest intelligence on the group, also known as ISIS or ISIL.
According to an assessment, the group has grown in size since the spring and its takeover of Mosul in northern Iraq as more fighters from around the world have mainly traveled to Syria to join its ranks.
The United States believes that while the group remains largely focused on its brutal takeover of large areas of Iraq, there is also an "expansion of its external terrorist ambitions."
Some foreign fighters are returning to their home countries with orders to "start new cells" of terrorist activity, the official said.
While some members may have a desire to attack the United States, the group's leadership is still focused on establishing an Islamic caliphate.
Still, they "see conflict with the United States as inevitable," the official said.
The United States believes a deadly shooting at Belgium's Jewish Museum in May by an alleged ISIS loyalist may be the kind of attack that could happen more often in western countries, possibly including the United States.
U.S. law enforcement is watching a small number of Americans for possible affiliation with the group.
ISIS foreign fighters may be operating somewhat independently of the organization's hierarchy, which the United States believes maintains lines of authority and even succession plans.
The intelligence community is now updating its assessment of how many fighters may be loyal to the group, and the number could be more than 10,000, the official said.
ISIS has taken advantage of the momentum it gained in Iraq over the past several months, resulting in a large number of new fighters joining up.
While it currently has funds from taking over oil facilities and other operations in Iraq, the United States believes that will not be enough to sustain ISIS if it tries to seize the entire country, the official said.
The United States also is watching closely to see whether and at what point ISIS loses support from Sunni loyalists in Iraq.
The U.S. calculation is that ISIS is taking advantage of its recent momentum. Because it is seen as "successful" in many areas, including Yemen and Africa where al Qaeda affiliates operate, they have gained support from some jihadists more widely.
In those areas, they also remain at odds with the core of al Qaeda in Pakistan led by Ayman al-Zawahiri and several of affiliates.
The thinking is as momentum slows, ISIS will be "under more pressure, reality sets in," the official said. "We don't see the group as 10 feet tall."