DONETSK, Ukraine—Apart from the sandbagged battle positions held by masked, pro-Russian gunmen wearing camouflage in cities across eastern Ukraine, an equally grave challenge for the country can be found here in a lightly guarded mansion, known in Soviet days as the House of Political Enlightenment.

It is here that Roman Lyagin, who doesn't hide his face, carries no weapon and wears a stylish black cardigan, is leading a political project that was inconceivable just weeks ago: a May 11 referendum that seeks to declare the Donetsk region—Ukraine's industrial heartland—a sovereign republic.

A similar effort is under way in the neighboring Luhansk region, where heavily armed men seized administrative buildings on Tuesday, then went on the local airwaves to urge people to come out and vote.

As town halls, police stations and state-security offices across Ukraine's restive east keep falling to pro-Russian militants, their strategy seems clear: Grab as much ground and infrastructure as they can to make sure the referendum takes place. That could give the relatively small separatist movement a veneer of legitimacy and pave the way for a further splintering of Ukraine, barely two months after the country lost Crimea to Russian annexation.

With the national government in Kiev looking increasingly helpless, the White House announced President Barack Obama would travel to Europe in June to consult with allies about the Ukraine crisis. His itinerary will include a stop in Poland, which has been urging a tougher line against Moscow.