KIEV, Ukraine — Army troops have penetrated deep inside a rebel-controlled city in eastern Ukraine in what could prove a breakthrough development in the four-month-long conflict, the Ukrainian government said Sunday.

However, the military acknowledged that another of its fighter planes was shot down by the separatists, who have been bullish about their ability to continue the battle and have bragged about receiving support from Russia. A column of several dozen heavy vehicles, including tanks and at least one rocket launcher, was spotted rolling through rebel-held territory Sunday.

Ukraine’s national security council said government forces captured a district police station in Luhansk Saturday after bitter clashes in the Velika Vergunka neighborhood.

Weeks of fighting have taken their toll on Luhansk, which city authorities say has reached the verge of a humanitarian catastrophe. The siege mounted by government forces has ground delivery of basic provisions to a halt and cut off power and running water.

Although rebel forces have regularly yielded territory in recent weeks, they have continued to show formidable fighting capabilities.

Ukrainian military spokesman Oleksiy Dmitrashkovsky said Sunday that the separatists shot down a Ukrainian fighter plane over the Luhansk region after it launched an attack on rebels. The pilot ejected and was taken to a secure place, he said. Another military spokesman, Andriy Lysenko, later said that the status of the pilot was still being clarified.

The column of armored vehicles was spotted southeast of Luhansk outside a town close to the Russian border and was heading west, deeper into rebel-held territory. It was unclear whether the column had come from Russia. Among the armored vehicles was a Strela-10, a short-range surface-to-air missile system capable of hitting targets up to 11,500 feet. The area is just across the border from where a large Russian aid convoy is poised to cross with supplies intended for Luhansk.