SNIZHNE, Ukraine — Two Ukrainian Su-25 fighter jets were shot down on Wednesday in eastern Ukraine near the Russian border. The planes were downed in an area of heavy fighting between government forces and Russian-backed separatists, near where a Malaysia Airlines jet was blown out of the sky last week, killing 298 people and drawing international dismay.

The Ukrainian government said the two fighter jets had been brought down near the village of Dmytrivka, east of Donetsk and about five miles from the Russian border, where government troops have been pushing hard to cut off the flow of fighters and supplies from Russia to the insurgents.

The government said the pilots of the fighter jets ejected safely. Government forces and insurgents appeared to be racing on Wednesday to find them.

Andriy Lysenko, a spokesman for the Ukrainian National Security and Defense Council, said the two jets had been hit by fire from the Russian side of the border. “The planes were shot down from Russian territory,” Mr. Lysenko said in a statement on Twitter.