WASHINGTON — American intelligence analysts have identified seven buildings in downtown Raqqa in eastern Syria as the main headquarters of the Islamic State. But the buildings have gone untouched during the 10-month allied air campaign.

And just last week, convoys of heavily armed Islamic State fighters paraded triumphantly through the streets of the provincial capital Ramadi in western Iraq after forcing Iraqi troops to flee. They rolled on unscathed by coalition fighter-bombers.

American and allied warplanes are equipped with the most precise aerial arsenal ever fielded. But American officials say they are not striking significant, and obvious, Islamic State targets out of fear that the attacks will accidentally kill civilians. Killing such innocents could hand the militants a major propaganda coup and alienate the local Sunni tribesmen, whose support is critical to ousting the militants, and Sunni Arab countries that are part of the fragile American-led coalition.

But many Iraqi commanders and some American officers say that exercising such prudence with airstrikes is a major reason the Islamic State, also known as ISIS or Daesh, has been able to seize vast territory in recent months in Iraq and Syria. That caution — coupled with President Obama’s reluctance to commit significant American firepower to a war the White House declared over in 2011, when the last United States combat troops withdrew from Iraq — has led to persistent complaints from Iraqi officials that the United States has been too cautious in its air campaign.