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Russia, Yanukovich's main backer, said it would not deal with Ukrainians who seized power from their elected leader in an "armed mutiny". It declared that Russian citizens' lives were under threat there, and contacted NATO to express concern.
With Ukraine's neighbours raising the alarm about a break-up of Ukraine, Moscow said the concerns of local leaders in Crimea and eastern Ukraine, Russian-speaking bastions of electoral support for Yanukovich, must be taken into account.
European Union foreign policy chief Catherine Ashton arrived in Kiev to discuss measures to shore up the ailing economy, which the finance ministry said needs urgent financial assistance to avoid default.
The EU has contacted the United States, Japan, China, Canada and Turkey to coordinate aid for Ukraine, a senior EU official said. France's foreign minister said an international donors' conference was being discussed.
U.S. Treasury Secretary Jack Lew and IMF chief Christine Lagarde agreed Ukraine would need bilateral and multilateral support for any reforms, a U.S. Treasury official said.
U.S. Treasury officials will accompany Deputy Secretary of State William Burns on a trip to Kiev this week.
Ukraine's parliament, exercising power as leaders try to form an interim government, replaced the head of the central bank, appointing lawmaker and former banker Stepan Kubiv.
Yanukovich, 63, who fled Kiev by helicopter on Friday, was still at large after heading first to his power base in the east, where he was prevented from flying out of the country, and then diverting south to the Crimea peninsula on the Black Sea, acting interior minister Arsen Avakov said.
"An official case for the mass murder of peaceful citizens has been opened," Avakov wrote on Facebook. "Yanukovich and other people responsible for this have been declared wanted."
Yanukovich had left a private residence in Balaclava, near the home base of Russia's Black Sea Fleet at Sevastopol, for an unknown destination, Avakov said. He went by car with one of his aides and a handful of security guards.
It was an ignominious political end for Yanukovich who has been publicly deserted by some of his closest erstwhile allies, stripped of his luxury residence near Kiev and had to witness the release from prison of his arch-rival Yulia Tymoshenko.
Russia recalled its ambassador from Kiev for consultations on Sunday, accusing the opposition of having torn up a transition agreement with the president it supported.
Prime Minister Dmitry Medvedev said Moscow had grave doubts about the legitimacy of those now in power in Ukraine and their recognition by some states was an "aberration".
"We do not understand what is going on there. There is a real threat to our interests and to the lives of our citizens," Medvedev was quoted as saying by Russian news agencies.
Russia cited a duty to protect the lives of its citizens in 2008 as one justification for military intervention in Georgia, another former Soviet republic, in support of Kremlin-backed separatists in South Ossetia.
On Independence Square in central Kiev, cradle of the uprising, barricades of old furniture and car tyres remained in place, with smoke rising from camp fires among tents occupied by diehards vowing to stay until elections in May.
The mood among the few hundred on the square was a mixture of fatigue, sorrow for the more than 80 people killed last week, and a sense of victory after three months of protests.
A large video screen by the side of the stage was showing the faces of the dead, one after another, on a loop.
"Now is not the time for celebrating. We are still at war. We will stay here as long as we have to," said Grigoriy Kuznetsov, 53, dressed in black combat fatigues.
Galina Kravchuk, a middle-aged woman from Kiev, was holding a carnation. "We are looking to Europe now. We have hope. We want to join Europe, " she said.
A day after Yanukovich fled, parliament named its new speaker, Oleksander Turchinov, as interim head of state. An ally of Tymoshenko, he aims to swear in a government by Tuesday that can run things until a presidential election on May 25.
Whoever takes charge faces a huge challenge to satisfy popular expectations and will find an economy in deep crisis, with state debt payments of around $6 billion due this year.
The Finance Ministry said it needed $35 billion in foreign assistance over the next two years and appealed for urgent aid in the next one or two weeks. It called for a donors' conference involving representatives of the European Union, the United States and the International Monetary Fund.
French Foreign Minister Laurent Fabius told reporters in Beijing the idea was under discussion and "this should be worked out in the coming days".
The cost of insuring Ukraine's debt fell on hopes that the country would now receive aid and avoid default, while bonds recorded gains on expectations that a new government would focus on the economy.
Ukrainian stocks soared to their highest since September 2012, But the hryvnia currency tumbled to a five-year low against the dollar as expectations grew the new government would focus on using dwindling foreign reserves to repay debt rather than defend the currency.
Scuffles in Crimea and some eastern cities between supporters of the new order in Kiev and those anxious to stay close to Moscow revived fears of separatism. A week ago those concerns were focused on the west, where Ukrainian nationalists had disowned Yanukovich and proclaimed self-rule.
President Barack Obama's national security adviser, Susan Rice, was asked on U.S. television about the possibility of Russia sending troops to Ukraine, which President Vladimir Putin had hoped Yanukovich would keep closely allied to Moscow.
"That would be a grave mistake," Rice said on Sunday. "It's not in the interests of Ukraine or of Russia or of Europe or the United States to see a country split."
Yanukovich's flight left Putin's Ukraine policy in tatters, on a day he had hoped eyes would be on the grand finale to the Sochi Olympics. The Kremlin leader spoke on Sunday with German Chancellor Angela Merkel, whose foreign minister had brokered a short-lived truce in Kiev on Friday.
They agreed Ukraine's "territorial integrity" must be maintained, Merkel's spokesman said.
It is unlikely the United States and its allies in NATO would risk an outright military confrontation with Russia, but such echoes of the Cold War underline the high stakes in Ukraine, whose 46 million people and sprawling territory are caught in a geopolitical tug of war.
In Russia, where Putin had wanted Ukraine as a key part in a union of ex-Soviet states, the finance minister said the next tranche of a $15 billion loan package agreed to in December would not be paid, at least before a new government is formed.