Recently, those calls have been toned down as the country gears up for repeat presidential elections on 26 December.
Nonetheless, analysts say the historical and cultural differences among the Ukrainian regions are likely to be reflected yet again in the new runoff between pro-Russian Prime Minister Viktor Yanukovych and his Western-leaning rival, Viktor Yushchenko.
Generally, people in the west speak Ukrainian and are more nationalistic. Those in the industrial east speak Russian, and their strong pro-Russian sentiments are largely absent in western Ukraine.
The west largely supports Yushchenko. The east and south mainly back Yanukovych.
Volodymyr, a coal miner in the eastern city of Donetsk, echoed a common perception there, telling RFE/RL his region would prosper if it didn't have to economically support the rest of the country.
"I support [autonomy plans because] we will live better than together with them, with western Ukraine," Volodymyr said.
Many dispute that claim, saying Donetsk actually receives more aid from Kyiv than it contributes in tax revenues.
But Nikolay Petrov, an analyst of Russian politics at the Carnegie Moscow Center, said that skewed perceptions are only part of the problem.
He said that history itself has created differences among the regions of Ukraine. The east for centuries was part of the Russian Empire while the western regions belonged to other European states.
"Western Ukraine is made of these territories, which were part of Poland, part of Austro-Hungary," Petrov said. "This is the reason for differences in language. In one case, [the language] is more 'Russified,' in the other case it has words that come from the Polish language. [History also brings] some differences in mentality and in political culture."
Oleksandr Lytvynenko, an analyst with the independent Kyiv-based think tank Rozumkov Center, said Ukraine attained its present borders only half a century ago -- too short a time to erase history's inheritance.
"In fact, Ukraine in its present borders exists from 1945, when Trans-Carpathian [territory] was annexed to it," Lytvynenko said. "And though during these 50 or 60 years some differences were removed, some still remain."
Lytvynenko said the Soviets encouraged different regions to be suspicious of one another. Soviet authorities distrusted Western Ukrainians because many fought against the Soviet Army during World War II and in the armed resistance afterward.
A similar attitude toward Westerners can still be found among people in the east.
Yet in a 1991 referendum, a majority of voters, even in eastern Ukraine, supported the country's independence.
And while eastern leaders earlier this month threatened to hold a vote on widening their regions' autonomy should Yushchenko take power, Yanukovych himself pledged yesterday to protect Ukraine's unity, regardless of the outcome of the upcoming repeat runoff.
For his part, Lytvynenko said he does not believe Ukraine's territorial integrity is threatened.
"There is no evidence indicating the opposition between the east and the west," Lytvynenko said. "Not only the western regions but also the central and northern regions -- from Kirovohgrad to Sumy - voted for Viktor Yushchenko, for the values he declares in his program and his speeches."
Lytvynenko said that no one in Ukraine, east or west, wants union with present-day Russia. But he said that people in the eastern industrial centers are nostalgic for the Soviet Union.
"The Soviet mentality is conserved here," Lytvynenko said. "It is a paradox but all pro-Russian feelings that exist here are based not on sympathies toward Russia, which is also 'capitalist and bourgeois' [as Ukraine], but on nostalgia for the Soviet Union."
Lytvynenko said that workers in this former Soviet hub of industry suffer from such nostalgia because they were once privileged. They were paid higher salaries and were proud to be upheld as model proletarians by Soviet ideologists.
Lytvynenko added that the interests of people in "pro-Russian" southern and eastern regions are actually quite distinct. He said that economic elites in all areas compete among themselves, while Donetsk miners have little in common with Russians from the southern Crimean Peninsula.
Petrov of the Carnegie Moscow Center agreed, he said that separatism is unlikely to become a serious political force in the near future.
"This separatism is observed in isolated regions, but I cannot imagine that macro-regional structures will emerge," Petrov said. "I can see little in common between, let's say, Crimea on one side, Donbass, on the other and Odessa on the third. There is little in common between them to allow them act united."
Although the east strongly backs Yanukovych, his rival is also courting voters there.
In a recent live interview on Ukrainian radio, Yushchenko held out the possibility that Russian could become an official language. He also stressed that Ukraine "is destined to pursue a policy of strategic partnership with Russia."
For more RFE/RL coverage and analysis of the political crisis in Ukraine, click here.