MOSCOW – The separatist demonstrations again churning through eastern Ukraine have raised fears of a Crimean-style invasion by the 40,000 Russian troops coiled just over the Russian border. But Moscow’s goals are more subtle than that, focused on a long-range strategy of preventing Ukraine from escaping Russia’s economic and military orbit, according to political analysts, Kremlin allies and diplomats interviewed this week.

Toward that end, the Kremlin has made one central demand, which does not at first glance seem terribly unreasonable: It wants Kiev to adopt a federal system of government giving far more power to the governors across Ukraine.

“A federal structure will ensure that Ukraine will not be anti-Russian,” said Sergei A. Markov, a Russian political strategist who supports the Kremlin.

Russian officials have said they envision a system in which the regions elect their own leaders and protect their own economic, cultural and religious traditions – including the forging of independent economic ties with Russia.

But many experts sharply dismiss the Russian plan as a stalking horse designed to undercut Ukrainian independence. “It is another way to dismantle and subjugate Ukraine,” said Lilia Shevtsova, an analyst with the Carnegie Moscow Center. “It means Moscow could grab and peel off any part of Ukraine at any time.”

President Vladimir V. Putin of Russia “wants Ukraine to be, one, absolutely neutral and, two, dependent on Moscow,” said Vladimir A. Ryzhkov, an opposition politician. “If you have a weak central government and strong governors, you can play directly with the governors over the head of Kiev.”

The United States, while supporting decentralization, has opposed giving too much power to the regions.

Russian officials are clear about their goals. “A centralized state will only be good for radicals,” said Sergei A. Zheleznyak, a deputy speaker of the Russian Parliament targeted for sanctions by the United States in March after pushing for the annexation of Crimea, using the shorthand favored by Russian officials to write off much of the Kiev government.

If Putin believes he is not getting his way on the constitution, he can be expected to take action before the Ukrainian presidential election scheduled for May 25, when a new government and a new constitution will be cemented, according to a broad range of analysts.

Some analysts are pointing to events surrounding the May 9 anniversary of the defeat of Germany in World War II, when huge emotional crowds fill the streets, as a possible catalyst for Russia to push the solution it wants.

While exactly what the Kremlin will choose to do in the weeks ahead is impossible to predict, analysts cited three potential outcomes.

In the first, Russia either manages to sway the presidential election with a candidate it favors, or it succeeds in putting in place the federal constitution it seeks in order to hold veto power over foreign economic and military policy.

The second outcome is a kind of Crimea Annexation Part II, with residents of the east and south voting in a referendum on whether to join Russia.

The third and least likely outcome is a full-scale military invasion.

Meanwhile, as armed standoffs persisted in eastern Ukraine, Putin tightened the economic screws on his impoverished neighbor by warning that Ukraine may have to pay in advance for gas imported from Russia.

The predominantly state-held Gazprom energy behemoth last week raised prices for Ukrainian purchases of its natural gas by 80 percent, canceling a discount that had been extended to Kremlin-allied former President Viktor Yanukovich last year.