In Sevastopol, residents told CNN they were angry that President Viktor Yanukovych has been forced out and fear that they will be oppressed by the country's new leaders.
Small pro-Russian protests were taking place in the Black Sea city Wednesday.
A CNN team in the area encountered more than one pro-Russian militia checkpoint on the road from Sevastopol to Simferopol.
Yanukovych's base of support is in eastern and southern Ukraine, where Russian culture and language predominate. In that region, most people are suspicious of the Europe-leaning views of their counterparts in western Ukraine, who were at the heart of the anti-government protests that filled central Kiev.
Many are struggling to come to grips with the rapid political upheaval that has unfolded in Ukraine in recent days, after months of protests and last week's bloody clashes between protesters and security forces.
Russia's Foreign Ministry has accused Ukraine's lawmakers of discriminating against ethnic Russians by excluding them from the reform process.
Talks on new government
The tensions come as Ukraine's lawmakers scramble to put together a new unity government amid continued instability after Yanukovych's ouster.
Vasil Gatsko, of the Ukrainian Democratic Alliance for Reforms (UDAR) party, said the newly formed government will be officially voted on in Ukraine's Parliament on Thursday morning. The interim authorities had initially hoped to announce a new government Tuesday.
The names of the nominees for the new administration were read in Kiev's Independence Square, or Maidan -- which has been at the heart of the protest movement -- for approval from the crowds gathered there. The nominees were selected in a meeting Wednesday of the three main opposition parties and smaller parties.
Bulatov, who was put forward as sports minister, spoke to CNN soon after the announcement. He is well-known as the activist who reappeared more than a week after he went missing amid anti-government protests, telling reporters he'd been kidnapped and tortured by his captors.
"People have to feel the changes, not to hear about them, but see them," he said.
When asked what he saw as his biggest challenge as a possible minister, Bulatov replied: transparency.
"I think the first thing I must do is to bring more transparency," he said. "It's gonna be the society, civil society I mean, who will be making decisions. The minister is a public person, and people must decide what is better, what are the priorities."
Lawmakers face the challenge of forming a body that genuinely represents of all the main political parties, despite their widely divergent views, and includes technical experts and some of the people's heroes from the protests in Independence Square.
Presidential and local elections are due to be held on May 25.
One candidate has already been announced. Opposition leader and former heavyweight boxing champion Vitali Klitschko, of the UDAR party, will run for the presidency, his press secretary Oksana Zinovyeva said.
Elite riot police disbanded
Earlier Wednesday, acting Interior Minister Arsen Avakov announced that a riot police force used against anti-government protesters in Ukraine had been disbanded.
Demonstrators accused the elite Berkut force, deployed by the government of Yanukovych to quell recent protests, of using excessive force.
Avakov said on his Facebook page that he'd signed the order disbanding the force Tuesday.
But the new, pro-Russian mayor of Sevastopol said Tuesday night at a rally in the city that he had secured funding to keep paying Berkut riot police there even after the force was disbanded.
The mayor, Alexej Chaliy, was elected in an unofficial local vote, but the interim authorities in Kiev have said he is not a legitimate leader.
Last week, the bloody street clashes between demonstrators and security forces left more than 80 dead, the deadliest violence in the country since it gained independence when the Soviet Union collapsed 22 years ago.
Russia, which backed Yanukovych, contends that the President was driven out by an "armed mutiny" of extremists and terrorists. A warrant has been issued for his arrest, but his whereabouts remain unknown.