It is possible that Russia will try to “break Ukraine into parts and leave Western Ukraine alone,” said Angela Stent, a specialist in Russia affairs at Georgetown University. But because that would leave a West-leaning government in Kyiv that Mr. Putin has previously depicted as illegitimate, she said, “I find it hard to imagine that.”

More likely, analysts said, is for Russia, at a minimum, to seek a constitution of Ukraine that grants significant independence to the east of the country, and an effective veto over Ukrainian government action.

The Ukrainians could agree to further elections—but the risk for Russia is that, even in the east, it wouldn’t like the outcome.

Mr. Clarke said one model of Ukrainian neutrality that might appeal to Russia is that of Austria in 1955. The Soviets pulled out of Austria in return for a constitutional guarantee of neutrality that exists today.