The Kremlin rushed reinforcements to the area last week, and Moscow’s defense ministry said later Monday that Ukraine had now lost about 1,600 troops in the operation, more than the number that military chief Gen. Valery Gerasimov said last week had attempted the incursion.

Putin said Monday that Ukrainian losses were “dramatically increasing.”

But the ongoing battles are a major blow to Putin’s internal standing, with the country’s influential military bloggers suggesting Monday that…