BEIRUT, Lebanon — The extremist militants of the Islamic State in Iraq and Syria have attacked Syrian troops with new ferocity in recent weeks, taking over three northeastern military bases, beheading scores of soldiers and seizing new territory.

The jihadist offensive has prompted some panicked supporters of the Syrian government to sharply criticize the leadership, questioning why it appeared to allow ISIS to build a base in the northern Syria province of Raqqa over the last year while claiming the Syrian Army was fighting terrorism. As far back as June, as ISIS fighters swept back into Syria with American weapons looted in Iraq, Elia Samaan, a government adviser, exclaimed, “Where is our air force?”

Now, the rising pressure from the militants, and from the Syrian government’s own supporters, is forcing President Bashar al-Assad’s forces to confront the possibility of a more direct battle with ISIS, a fight that had not appeared to be the government’s top priority even as the group amassed fighters and resources that helped it seize a swath of territory stretching across the border and into Iraq.

The escalating confrontation between Mr. Assad’s forces and ISIS is another indication of just how much the rise of the radical group has erased borders and upended alliances around the region, and the world. President Obama, who has long called for the ouster of Mr. Assad, is facing similar pressure to attack ISIS inside Syria after his top military adviser said the group cannot otherwise be defeated.