An extremist group allied with Islamic State has emerged as a potent force on the battlefield in northern Afghanistan, threatening to further destabilize the country and sow instability throughout Central Asia, senior Afghan officials say.

The Islamic Movement of Uzbekistan, or IMU, designated a foreign terrorist organization by the U.S., has been on the front lines of a major anti-government offensive this summer in the north. And that worries both Kabul and its neighbors, as the violence has swept across the Afghan provinces that border the former Soviet republics of Turkmenistan, Uzbekistan and Tajikistan.

“Why are they going that way?” said Hanif Atmar, the national security adviser to Afghan President Ashraf Ghani. “Because they want to be closer to Central Asia, which is exactly where they want to be,” he added.

“Afghanistan is fighting on behalf of Central Asia,” Mr. Atmar said.