When a Ukrainian armored column approached the town last Wednesday and then swiftly surrendered, a group of disciplined green men suddenly appeared on the scene and stood guard. Over the course of several hours, several of them told bystanders in the sympathetic crowd that they were Russians. They allowed themselves to be photographed with local girls, and drove an armored personnel carrier in circles to please the crowd.

“It’s hard to fathom that groups of armed men in masks suddenly sprang forward from the population in eastern Ukraine and systematically began to occupy government facilities,” Gen. Philip M. Breedlove, NATO’s top military commander, wrote in a blog post on the alliance’s website.“It’s hard to fathom because it’s simply not true. What is happening in eastern Ukraine is a military operation that is well planned and organized, and we assess that it is being carried out at the direction of Russia.”

His evidence, however, was mostly circumstantial: Pro-Russian gunmen “exhibit telltale military training and equipment”; they handle weapons like professional soldiers, not new recruits to a pickup “self-defense” force; they carry weapons and equipment that are primarily Russian Army issue, not gear “that civilians would be likely to be able to get their hands on in large numbers.” General Breedlove conceded that such points, taken alone, might not prove much, “but taken in the aggregate, the story is clear.”

Heightening skepticism of Russia’s denials is also the fact that Mr. Putin, after denying any Russian link to the masked gunmen who seized government buildings in Crimea and blockaded Ukrainian military bases there, last week changed his story and said, “Of course, Russian servicemen did back the Crimean self-defense forces.”

More direct evidence of a Russian hand in eastern Ukraine is contained in a dossier of photographs provided by Ukraine to the Organization for Security and Cooperation in Europe, a Vienna-based organization now monitoring the situation in Donetsk and other parts of the country. It features pictures taken in eastern Ukraine of unidentified gunmen and an earlier photograph of what looks like the same men appearing in a group shot of a Russian military unit in Russia.

One set of photographs shows what appears to be the same gunman in pictures taken in the Crimean annexation and more recently in Slovyansk. Another features a portly bearded man photographed in Slovyansk on April 14, wearing a camouflage uniform without insignia. Six years earlier, he had been photographed during Russia’s invasion of Georgia with a Russian special forces patch on his left arm.

Another character in Ukraine’s case against Russia is Mr. Strelkov, the alleged military intelligence officer who Kiev says took part in a furtive Russian operation to prepare for the annexation of Crimea and, more recently, in insurgent action in Slovyansk.