Disrupting the ability of the group calling itself the Islamic State to raise funds through oil revenue is a key U.S. military objective, an official said.

U.S. Central Command said this week a series of airstrikes were carried out against the group variably known as the Islamic State of Iraqi and the Levant. Strikes inside Iraq and Syria were carried out with the support of Middle East and European allies.

Jen Psaki, a spokeswoman for the U.S. State Department, said there are targets outside the strategic border town of Kobani that require military attention.

"The transfer of oil or the ability of ISIL to gain funding and increased strength from oil revenues is of great concern," she said during a Wednesday press briefing. "That's one of the reasons why we've gone after the refineries, and that's one of the objectives of our efforts."

Peace advocates last month said disrupting oil financing may be a better strategy to contain the militant group than military strikes. The Islamic State at its peak was said to be generating about $2 million per day on pilfered oil.

The militant group claimed a brief hold over the Baiji oil refinery north of Baghdad in mid-June.