Mitt Romney says the decision to pull international military personnel from Afghan ministries is "an extraordinary admission of a failure" to establish strong ties for a successful transition to Afghan security leadership.
The move came after a gunman killed two American military advisers Saturday inside a ministry building.
More than 30 people have died in clashes since it became known last week that copies of the Muslim holy book and other religious materials were thrown into a fire pit used to burn garbage at a U.S. base near Kabul.
President Barack Obama has apologized for what he said was a mistake.
Romney tells "Fox News Sunday" that for many in the U.S., the apology "sticks in their throat" because many Americans have died trying to help Afghans "achieve freedom."