“The percentage of I.E.D. attacks compared to overall rebel activity has not increased in a statistically significant way,” Mr. Holliday wrote by e-mail, just hours before the assassinations in Damascus. “What has increased is the percentage of effective attacks.”

But, he added, “what has increased the most, and this has been the hardest thing to put a finger on through open source research, is the number of what U.S. military might call ‘catastrophic’ I.E.D. attacks.”

By that he meant bombs that destroyed heavily armored tanks, or caused large numbers of casualties.

Although precise casualty estimates are impossible to obtain, one senior Obama administration official who spoke on the condition of anonymity under administration practice said that by June the Syrian military was suffering an average of 20 dead soldiers a day in various types of attacks, and several times that number of wounded. This would be a significant drain on a force already suffering from defections and now trying to suppress an escalating guerrilla conflict by conventional means.

The exact means by which anti-Assad fighters have improved their manufacture and use of bombs, and who trained them, is not clear.

Mr. Holliday said the capability “comes in part from the expertise of Syrian insurgents who learned bomb-making while fighting U.S. troops in eastern Iraq.”

An American official who follows the fighting in Syria and spoke on the condition of anonymity noted another example of turnabout. Some of the expertise, the official said, appeared to have been derived from the very trainers in explosives, who were formerly in Syrian intelligence or under its tutelage, with which Syria for decades exported bomb-making and other lethal skills to groups it sponsored in neighboring states.

The official also said the United States government strongly suspected the use of explosively formed penetrators, or E.F.P.’s, bombs with a shaped charge that can penetrate tank armor and that have often been associated with Iran. The official said that the number of these bombs in use was very small, and that the technology for making them was widespread enough that their presence did not indicate Iranian support for the rebels, who are seeking the ouster of an Iranian ally.