The Ukrainian army was making gains in its battle to retake Horlivka, a city outside the rebel stronghold of Donetsk, and fighting extended to the outskirts of Donetsk. The military has said it is preparing to advance into Donetsk, one of two epicenters of the insurgency that has raged since spring. Ousting the rebels from their self-proclaimed Donetsk People’s Republic would be a major victory for the Ukrainian government, and would signal that pro-Russian separatists were nearing the end of their campaign to break away from Ukraine.