WASHINGTON—Russia’s expanding military deployments in and around eastern Ukraine in recent days are setting the stage for a new phase of Moscow’s offensive—one that is likely to be very different from the kind of fighting that has characterized the past two months.

This time, the two countries’ militaries will be operating on open terrain well-suited for massed forces and armored thrusts. Russian forces will also be fighting in closer proximity to their bases in western Russia, giving them shorter supply lines, and on territory their commanders know better.