Belarus, which depends on Russian supplies of cheap energy to keep its economy afloat and shares Mr. Putin’s belief that the West is plotting to sow division and even to invade, says it has no such concerns itself.

Military exercises, including those conducted by NATO, often feature invented enemies, a practice that blurs their real purpose and avoids upsetting real countries that do not like to be used as a punching bag for military training — especially when this involves simulated nuclear attacks. Western experts say they believe that Russian war games in 2009 and 2013 included simulated nuclear strikes against Warsaw and Stockholm.

The three fake countries at the center of the Zapad-2017 drills, however, have taken on a virtual life of their own online. While it is not clear who is behind it, a clearly pro-Western satirical Twitter account issues regular announcements in the name of the Veishnoriya Ministry of Foreign Affairs and displays pictures of the fake country’s passport, flag, national currency and other national symbols, all of them invented.

“We are deeply concerned about the concentration of Belarusian military equipment at the borders of Veishnoriya,” reads one message posted by the nonexistent nation’s Foreign Ministry. Others include a call for volunteers from “brotherly countries” to repel an invasion from the east and warnings that Veishnoriyans are “warlike beasts” who will not surrender.

Veishnoriya also has a lively account on Vkontakte, the Russian equivalent of Facebook, with posts of beautiful Veishnoriyan women and natives in what is said to be traditional Veishnoriyan clothing. It also has fierce supporters on Facebook, where one fan provided a tongue-in-cheek “historical note” about the nonexistent country’s martial spirit: “Throughout its history, Veishnoriya hasn’t lost a single war.”

Russia has dismissed Western anxieties over Zapad-2017, saying that the exercises are purely defensive. Fueling unease is Russia’s silence on what exactly the exercises will involve. Belarus has invited foreign military attachés based in Minsk to watch and released some details of its war games with Russia, including airstrikes and tank battles on Sunday and Monday.

But it is not clear that the attachés will have the freedom they need to move about and to talk with soldiers. Moscow, for its part, has said only that the exercises threaten nobody and will involve operations in Belarus, in Russia’s Western Military District and in the Russian enclave of Kaliningrad, next to Poland.