Kurdish forces pushed Tuesday to retake territory they lost over the weekend to the Islamic State in a major counteroffensive that will test the ability of the best-trained military force in Iraq to confront the radical Islamist group.

Kurdish forces made up of thousands of insurgents from Turkey and Syria attacked Islamic State positions at Sinjar, one of three Iraqi cities that fell to the Islamic State over the weekend, while peshmerga militias loyal to Iraq’s autonomous Kurdistan Regional Government pressed to lift the Islamic State’s siege of the Mosul Dam, Iraq’s largest and an important source of electricity. The Islamists almost overran the dam over the weekend.

U.S. officials said they were working with the Kurdistan Regional Government in Irbil and Iraq’s central government in Baghdad to counter the Islamic State’s advance. But it was unclear what materiel assistance, if any, the United States was lending to the fight. […]