ERBIL, Iraq—The government of Iraq’s semiautonomous Kurdistan region, a crucial front-line partner in the U.S.-led coalition against Islamic State, is confronting a shortage of weapons and growing economic disquiet among its citizens and foreign investors in the oil-rich area.

“After what happened with ISIS, things have become really difficult—it’s not easy,” said Kurdistan Prime Minister Nechirvan Barzani in an interview with The Wall Street Journal, using another name for Islamic State.

Kurdish officials say the local military force known as the Peshmerga hasn’t yet received from the West any of the heavy weapons it needs to fight Islamic State on multiple battle fronts, with the exception of a recent shipment of German antitank missiles.

In the Kurdistan region, foreign investors including Western oil companies are scaling down operations and laying off local staff, according to several officials. Many major construction and infrastructure projects are at a standstill because contractors haven’t been paid, while the regional government scrambles to find new revenue sources and tackle a bloated public-sector payroll estimated to account for about 75% of government expenditures.

Mr. Barzani said contractors working on projects throughout the region are demanding money that is increasingly hard to come by. “It’s a big problem now, we have to pay the companies about $1.5 billion,” he said.