But "surgical strikes" against Ukrainian military forces deemed responsible for the attacks, as claimed by an anonymous Kremlin official in the major Moscow daily Kommersant? That's "nonsense," Vladimir Putin's spokesman said on Monday.
Experts say the conflicting signals coming out of the Kremlin show just how at odds it is with itself over what to do in eastern Ukraine, as conditions deteriorate and ferocious fighting bumps up against the long and relatively open border with Russia.
One faction, they say, advocates direct Russian action to support east Ukraine's beleaguered rebels – either by imposing a no-fly zone over the embattled region, or through pinpoint attacks on Ukrainian artillery units that are accused of firing on Ukrainian civilians and, occasionally, Russian ones too.
"When Israel reacts to provocations with an all-out attack on Gaza, the world is quite understanding about that," says Vladimir Zharikhin, deputy director of the Kremlin-funded Institute of the Commonwealth of Independent States in Moscow. "But Russia is supposed to sit back and take it? Our investigators have found shell fragments in the village that was attacked, and we know that only Ukrainian forces have artillery of this caliber. Russia is a great power, and it doesn't have to put up with this sort of thing in its backyard."
The other Kremlin faction, which appears to have the upper hand at the moment, favors caution. They argue that direct Russian intervention would only give Ukrainian President Petro Poroshenko the rallying point he wants, and a winning argument for greater Western assistance. Instead, they say, Russia holds most of the cards in any long-term settlement for Ukraine. Moscow can afford to wait as the Poroshenko government muddles through what promises to be a long and bloody counter-insurgency in the country's east, even as Ukraine careens toward economic implosion.
"The Kremlin does not have a master plan for what to do in Ukraine; it's mostly reacting to events," says Andrei Kortunov, director of the Russian International Affairs Council, a think tank with strong connections to the Russian Foreign Ministry. "The dominant view right now is that we should let Poroshenko reap the consequences of the military campaign he chose to embark on. It's easy to start a conflict like this, very hard to finish it up."
Mr. Kortunov says that Russia needs to stress its role as a diplomatic player, and as the huge neighbor Ukraine needs to rebuild its shattered economy and reconcile with embittered eastern Ukrainians.
"The pendulum will swing back in Ukraine, perhaps in unexpected ways. Russia can afford to wait," he says.
Kiev denies that its forces shelled the Russian border village Sunday and insists that it was the work of pro-Russian rebels. Ukrainian defense officials warn that Russia is stepping up "provocations" on the frontier, and has been allowing ever more pro-rebel volunteers and military equipment to cross into the embattled territory from Russia. Ukraine's best-known military expert, Dmitry Tymchuk, predicted on his Facebook page today that all signs point to a full-scale Russian invasion of Ukraine on Tuesday.
"Opinion in Russia is badly split over what to do about this. But so far, despite all the growing pressures, it seems that Putin has decided that the long-term price of intervening directly is too high," says Dmitry Polikanov, vice president of the PIR Center, an independent security think tank in Moscow.
"It's not just that our relations with the West would be greatly aggravated, it's also that we can't really afford the costs of peace-building in eastern Ukraine afterwards," Mr. Polikanov says. "Our best option now is to strengthen the border, and wait to see what will happen next. The ball is in Poroshenko's court."