Ukraine's interim authorities have launched a presidential campaign, are working on a new government and are trying to seek immediate financial help from the West.
But protests in the country's pro-Russian region of Crimea and the shooting of a top aide to fugitive president Viktor Yanukovych - a man despised by protesters - have raised fears of divisions and retaliation.
Andriy Klyuyev, the chief of staff for Yanukovych until this weekend, is in hospital after being shot on Monday. It is not clear where in Ukraine the shooting took place.
At the Ukrainian parliament in Kiev, authorities delayed the formation of a new government until Thursday, reflecting the political tensions and economic challenges the country faces after Yanukovych fled the capital and went into hiding.
Parliament speaker Oleksandr Turchinov, who was named Ukraine's interim leader, is now nominally in charge of the country of 46 million whose ailing economy faces a possible default and whose loyalties are torn between Europe and long-time ruler Russia.
Law enforcement agencies have issued an arrest warrant for Yanukovych over the killing of 82 people, mainly protesters, last week in the bloodiest violence in Ukraine's post-Soviet history. The president fled after signing a deal with opposition leaders to end months of violent clashes between protesters and police.
Parliament has adopted a resolution urging the International Criminal Court in The Hague to bring Yanukovych and other top Ukrainian officials to justice for the violent crackdown on protesters.
The protests erupted after Yanukovych's abrupt decision in November to reject an agreement to strengthen ties with the European Union and instead sought a bailout loan from Moscow. But they grew into a massive movement demanding less corruption and greater human rights.
Parliament has fired some of Yanukovych's lieutenants and named their replacements, but it has yet to appoint the new premier or fill all remaining government posts. Yanukovych's whereabouts are unknown. He was last reportedly seen in the Crimea, a pro-Russia area.
Nationalist protesters, meanwhile, have removed a Soviet star from the top of the Ukrainian parliament building, the Verkhovna Rada.
The European Union's top foreign policy official, Catherine Ashton, urged Ukraine's new government to quickly work out an economic reform program so the West could consider financial aid to keep Ukraine from bankruptcy.
After meeting with Ukraine's interim authorities in Kiev, she also said the new government should not exclude members of Yanukovych's Party of Regions.
"It needs to be inclusive," Ashton told reporters.
Turchinov has said closer integration with Europe and financial assistance from the EU will be "key factors in (Ukraine's) stable and democratic development."
Russian Prime Minister Dmitry Medvedev has strongly condemned Ukraine's new authorities, saying they came to power as a result of an "armed mutiny".
The campaign for Ukraine's early May 25 presidential election has begun, with Yanukovych's archrival, former Prime Minister Yulia Tymoshenko, widely seen as a top contender for the post.
Opposition leader Vitali Klitschko, the former heavyweight boxing champion, has announced his candidacy. But Tymoshenko, who was freed on Saturday after spending two-and-a-half years in prison on charges that many in the West called politically tainted, has not yet declared whether she will run.
Tymoshenko has been taking part in the negotiations on forming a new government, her daughter, Eugenia Tymoshenko, said.
"She barely sleeps now and everything she tries to do is to make sure that first of all the opposition is unified, that everyone is trying to act on behalf of the people of Ukraine."
She would not comment on whether her mother plans to run for president. She said her mother plans to spend a week in Germany in March to undergo treatment for a back problem.