MOSCOW — The war in eastern Ukraine that simmered quietly for months has erupted in a lethal bout of fighting in recent days.

The violence, which killed at least eight Ukrainian soldiers and three on the pro-Russian side, shifted the front lines by only a few hundred yards in several spots, but potentially complicates American efforts to improve relations with Russia.

The United States Army helps to train and equip Ukrainian soldiers, who are fighting Russian-backed separatists in two eastern provinces of Ukraine, in the only active war in Europe today.

In the latest outbreak, the sides vied for control of what are known as “gray zone” territories, areas between the front lines that had previously been in buffer zones.