WASHINGTON—The U.S. is in talks with North African countries about positioning drones at a base on their soil to ramp up surveillance of Islamic State in Libya in what would be the most significant expansion of the campaign against the extremist group in the region.

The establishment of such a base would help eliminate what counterterrorism officials described as one of the last and most pressing intelligence “blind spots” facing U.S. and Western spy agencies. Washington and its allies are seeking to contain the expansion of Islamic State beyond Iraq and Syria, where a U.S.-led military campaign against the group is already under way.

“Right now, what we are trying to do is address some real intelligence challenges,” a senior administration official said. A base in North Africa close to Islamic State strongholds in Libya would help the U.S. “fill gaps in our understanding of what’s going on” there, the official added.

The quest for a base represents an acknowledgment that the extremist group has managed to enlarge its area of influence even while under U.S. and allied bombardment in Iraq and Syria.

Islamic State has claimed a number of attacks in North Africa recently, including the killing of dozens of foreign tourists at a Tunisian beach resort last month. The attacker may have trained in Libya with a militant group sympathetic to Islamic State.