The first wave of U.S. military attacks against ISIS has cost nearly $1 billion, according to a military think tank.

And costs could rise to as much as $1.8 billion a month if the U.S. military presence grows to 25,000 ground troops, as some have suggested, said the Center for Strategic and Budgetary Assessment (CSBA).

U.S. air strikes started in Iraq last month and expanded to Syria last week.

So far U.S. military efforts have mostly been limited to air strikes. There are also 1,600 U.S. troops in Iraq serving in advise-and-assist roles and staffing the joint operation centers. However, they aren't conducting combat operations against ISIS.

President Obama said he has no plans for U.S. ground troops to engage in combat.

Related: ISIS fighter says U.S. airstrikes aren't effective

The Center said that even if operations don't escalate, it will cost between $200 million and $320 million a month to maintain the current level of airstrikes and support troops. That works out to as much as $4 billion a year.

A Pentagon spokesman told CNN last week that military operations are likely to continue at their current level "for a matter of years.