Michael A. McFaul, President Obama’s former ambassador to Moscow who is now a professor at Stanford University, said Mr. Putin had frequently shifted between more pragmatic calculations and a nostalgia-tinged commitment to reviving Russian power, particularly over former Soviet territories like Ukraine. “Putin has always had dual impulses, lamenting the collapse of the Soviet Union but also recognizing that Russia has to integrate in the wider world,” Mr. McFaul said in a telephone interview.

Russia has already cut off gas supplies to Ukraine, complaining that it has not been paid for previous deliveries, and energy shortages will grow increasingly painful for Ukraine with the approach of winter. Moscow’s long-term goal, analysts say, is not to force Ukraine to recognize the rebels’ self-declared states, which even Russia does not recognize, but to ensure that Ukraine never joins NATO or allows Western troops on its territory.

But Western officials said that instead of pulling back from its military involvement, Russia had stepped up its activities to help pro-Russian rebels mount counterattacks and break the momentum of a Ukrainian offensive in the east.

Ukraine greeted Tuesday’s meeting in Minsk, held in a marble-clad hall dripping with chandeliers, as a singular opportunity to end, or at least curtail, a conflict that has killed more than 2,000 people in eastern Ukraine, as well as nearly 300 people aboard a Malaysia Airlines jet shot down over rebel-held territory in July.

“Today in Minsk, without any question, the fate of the world and the fate of Europe are being decided,” Mr. Poroshenko said in an opening speech to the presidents of Russia, Belarus and Kazakhstan, the three members of the Eurasian Customs Union, and officials from the European Union.