It is essential that further expansion of the campaign against ISIS and other militant groups be debated rigorously and openly by Washington and its coalition partners. For one thing, it is dangerous and unwise to assume that “affiliates” pledging support for ISIS are controlled by ISIS, share its resources or can duplicate its ruthless skills. Many cannot do so, and the coalition would make a serious mistake if it treated all splinter groups as the same kind of threat.

Image Egyptians inspected the damage of an attack in January by a group allied with the Islamic State. Credit... Alaa Elkamhawi/Almasry Alyoum, via European Pressphoto Agency

In any case, the problem is far more complicated than just going after ISIS and its affiliates. There are many threats ravaging and destabilizing the Middle East, North Africa and Central Asia, including not only extremistists (some allied with ISIS, many not) but also stubborn, long-standing sectarian conflicts and, in some failed states like Yemen and Libya, the near-total collapse of governmental authority and civil order. That makes finding a coherent and effective strategy — or more likely strategies — to deal with these challenges much harder.

What is manifestly clear is that while America can and should play a leading role, the main responsibility for confronting extremist groups and ending sectarian wars lies with countries in the region, including Saudi Arabia and Iran. That will require them to put aside enmities, cooperate and take on more of the fight. It will also require many of them to make reforms at home, where radical ideology and repressive governance foster extremism.

A Pentagon official played down the possibility of an expanded war. But the fact that it is under discussion should be of more than passing interest to a public grown tired of war. The spread of extremism will be the focus of several meetings in the next few months, including a summit meeting of Arab leaders called by President Obama for this month and a meeting of coalition military commanders to be convened by the United States Central Command.

In some ways, Mr. Obama has sought to limit the American role in the anti-ISIS fight by ruling out ground troops and, at first, limiting military involvement in Iraq to air strikes and keeping force levels down, just enough to provide intelligence and to help train and advise Iraqi units. But he has since increased troop levels in Iraq and expanded air strikes into Syria. He also recently asked Congress to approve legislation that would give him, and his successors, what appears to be an open-ended mandate to wage war against ISIS and “associated persons or forces.”