Chairman of the Joint Chiefs of Staff Martin Dempsey said Thursday that Russian President Vladimir Putin’s new use of Russian military force inside Ukraine harkens back to 1939 when Joseph Stalin led a Russian invasion of Poland, and Dempsey predicted Putin was far from finished.

Dempsey was speaking to the Aspen Security Forum and responding to the news that the U.S. government is accusing the Russian military of firing artillery from Russian territory into eastern Ukraine in support of separatists there. The latest development represents a dangerous escalation of the crisis on the part of Putin, and the Russia-Ukraine crisis is now a global problem, he said.

“It does change the situation. You’ve got a Russian government that has made a conscious decision to use its military force inside another sovereign nation to achieve its objectives. It’s the first time since 1939 or so that that’s been the case,” Dempsey said. “They clearly are on a path to assert themselves differently not just in Eastern Europe, but Europe in the main, and towards the United States.”

Since 2008, the Russian military has increased its capability, proficiency, and the level of its activities, indicating Putin’s worldwide ambitions, Dempsey said. The strategy is Putin’s alone, he added, and said much of Russia’s military were probably reluctant participants in Putin’s war.

“This is very clearly Putin, the man himself, with a vision for Europe as he sees it, what he considers to be an effort to redress grievances that we burdened upon Russia after the fall of the Soviet Union and also to appeal to ethnic Russian enclaves across Eastern Europe,” he said. “He’s very aggressive about it, he’s got a playbook he’s been successful with two or three times, and he will continue.”

Following new U.S. and European sanctions on Russia last week and amid harsh international criticism of Russian support for Ukrainian separatists who apparently accidentally shot down a commercial airliner, Putin has not shown any indication that he is responding to the pressure by pulling back, Dempsey said.

“At a time when some folks could convince themselves that Putin would be looking for a reason to de-escalate, he’s actually taken a decision to escalate,” Dempsey said

Joseph Stalin used similar rhetoric and justifications when he invaded Poland in September 1939, only days after Adolf Hitler’s Nazi army invaded Poland from the other direction. Stalin and Hitler had signed a secret pact of non-aggression and proposed to carve up Europe between them, but Stalin said his goal was to protect ethnic Russians in his near abroad.

“The Soviet Government cannot regard with indifference the fact that the kindred Ukrainian and White Russian people, who live on Polish territory and who are at the mercy of fate, are now left defenseless,” read the note from the Soviet Foreign Ministry to the Polish Ambassador to Moscow on the day Stalin invaded.

Putin has not yet ordered a full-on Russian military invasion of eastern Ukraine, but continues to ship heavy weapons including tanks and rocket launchers to Ukrainian separatists from the Russian military base in Rostov, according to U.S. intelligence officials, along with what Dempsey called a strategy of “proximate coercion and subversion” inside Ukraine that is creating dangerous conditions.

“Putin may actually light a fire that he loses control over,” he said. “There’s a rising tide of nationalism in Europe right now that has been created in many ways by these Russian activities.”

State Department deputy spokeswoman Marie Harf told reporters Thursday that U.S. intelligence showed that the Russian military had now fired artillery from Russia into Ukraine, but she declined to provide any details about the source of the intelligence.

“We have new evidence that the Russians intend to deliver heavier and more powerful, multiple rocket launchers to the separatist forces in Ukraine, and have evidence that Russia is firing artillery from within Russia to attack Ukrainian military positions,” she said. “This is just some pieces of info I’ve been able to get from our intelligence friends for you. I can’t tell you what the information is based on. I know that’s disappointing to you.”

Mikheil Saakashvili, the former president of Georgia who fought a war against Russia in 2008, told The Daily Beast in an interview that as the Ukrainian government escalates its war on the separatists, Putin is escalating his support of them in proportion, a strategy he has employed since the crisis began.

But although everything was going Putin’s way for a while, recently the Ukrainian government has been performing much better, he said, and the downing of MH17, apparently by the separatists, also could lead to more sanctions against Russia. Putin is cornered, according to Saakashvili, which is why he is lashing out.

“Putin’s problem is that he is right now on the verge of military defeat. So he has two choices right now, neither of them good,” Saakashvili said. “He could move in his troops, after which he would become an international pariah with no certain outcome. The second choice he has is to live with military defeat, but that could trigger a process inside Russia that he can no longer control… Putin cannot afford to lose.”