Among the calls: More aggressively arming Sunni tribes and Peshmerga forces who oppose Islamic State, also known as ISIL and ISIS.

“If there comes a time when we have to change the kinds of support we give we will make that recommendation,” Mr. Carter said in an interview with CNN aired Sunday.

House Armed Services Chairman Mac Thornberry (R., Texas) said on ABC’s “This Week” that the battle in Ramadi was among the many reasons why he doubted the Obama administration’s claim that U.S. efforts have succeeded in degrading the strength of ISIS.

“I don’t see evidence of that,” said Mr. Thornberry. “I see ISIS gaining territory in Iraq and Syria.” What is more, he said, “their ideology, their approach, their brand is growing faster than their territory.”