The split reflects a rising concern that the Islamic State poses a more immediate danger because of its unprecedented social media campaign, using sophisticated online messaging to inspire followers to launch attacks across the United States.

Many intelligence and counterterrorism officials warn, however, that Qaeda operatives in Yemen and Syria are capitalizing on the turmoil in those countries to plot much larger “mass-casualty” attacks, including bringing down airliners carrying hundreds of passengers.

This is not an academic argument. It will influence how the government allocates billions of dollars in counterterrorism funds, and how it assigns thousands of federal agents, intelligence analysts and troops to combat a multipronged threat that senior officials say is changing rapidly.