BEIRUT, Lebanon — Far from being depleted by its recent sweep into Iraq, the extremist Islamic State in Iraq and Syria is pressing deeper into Syria, regaining territory it had lost to the mainstream Syrian insurgents just as the Syrian Army has come within five miles of encircling the insurgent-held section of Aleppo, Syria’s largest city.

The dual advance is on the verge of dealing a potentially fatal blow to the mainstream insurgents, leaving them besieged in the city while ISIS, a group deemed too extreme even by Al Qaeda, faces the Syrian government across a crucial front line at the city and surrounding province of Aleppo, the linchpin of northern Syria.

The developments, some of the most strategically important in Syria’s three-year war, come as the American military for the first time strikes ISIS fighters in Iraq. The United States says it aims to prevent massacres of Iraqi civilians, but apparently has no plans to strike the group in Syria, where it incubated into perhaps the world’s most dangerous Islamist extremist group.

That seeming contradiction highlights the messy snarl of conflicts sweeping the region: The United States now views ISIS as a global threat, a position that places America notionally on both sides of the bitter conflict in Syria, where both the insurgents and the government claim to be fighting the group.