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Yanukovich, caught in a tug of war between Russia and the West, is seeking a way out of a sometimes violent confrontation with protesters who have occupied city streets and public buildings following his decision in November to spurn a trade deal with the EU and accept financial aid from Moscow.
As he returned to work a day before parliament begins a new session, the political opposition, buoyed by fresh expressions of support from Western governments, pressed for further concessions to end the street protests.
The president's first urgent task, after an absence that some saw as a tactical gambit to gain time, will be to name a new prime minister to succeed Mykola Azarov, who stepped down on Jan. 28 under pressure from the protest movement.
But Yanukovich confined himself, in his first public appearance since Wednesday, to warning against the actions of thousands of protesters who have erected barricades around central Kiev and occupied public buildings there and in other cities, as well as militants who have clashed with police.
At least six people were killed in clashes last month.
"We must say no to extremism, radicalism, the fanning of enmity in society, which is the basis of the political fight against the authorities," he said in comments to an international symposium that were carried on his website.
The speaker of parliament, an ally of Yanukovich, told lawmakers on Monday that the president was still planning to discuss the choice of premier with the opposition and may propose someone this week.
In other concessions, Yanukovich last week approved the repeal of recent anti-protest laws and offered a conditional amnesty to activists who have been detained in the unrest.
But opposition leaders want further concessions, including a broader amnesty to free all those detained and a return to an earlier constitution, which would curb Yanukovich's presidential powers and give greater control to parliament over the formation of governments.
European Union foreign policy chief Catherine Ashton was due in Kiev for talks with Yanukovich and separately with opposition leaders on Wednesday. She is reported to have said the EU and United States are preparing a package of economic support that would be available to Ukraine if it embarks on a transition to a new political system and new elections.
Such support could be needed if Russia froze a $15-billion package it offered Yanukovich after he refused to sign the deal with the European Union. Having lent $3 billion so far, Moscow suspended a further tranche of $2 billion, saying it first wants to see which new government Yanukovich appoints.
In a worrying development for Ukrainians in the grip of an Arctic winter, energy firm Naftogas said it might not be able to pay Gazprom for Russian gas imports on which the former Soviet republic relies.
Easier terms for energy after years of "gas wars" with Kiev were part of Moscow's support package agreed two months ago.
Russia, which had threatened Ukraine with ruinous trade sanctions if it signed up to last year's EU pact, has been concerned to maintain its influence over the country of 45 million. It accused Western-backed opposition leaders on Monday of provoking unrest by calling for "volunteer militias".
"We expect the opposition in Ukraine to avoid threats and ultimatums and join in dialogue with the authorities in order to find a constitutional way out of the country's deep crisis," the Russian foreign ministry said in a statement.
With relations between the West and President Vladimir Putin's Kremlin already strained over a variety of issues, the fate of Ukraine, the biggest state lying between central Europe and Russia, has raised fears of broader instability across the continent if the standoff in Kiev should spiral out of control.
"All our partners both in the East and in the West understand the threat to their countries if the political crisis is not overcome and grows," Ukrainian Foreign Minister Leonid Kozhara said in comments to reporters. "The action of radical groups which are acting openly gives special concern."
Tensions between Ukraine's Russian-speaking east and Ukrainian-speaking west are evident in small groups on either side which draw on historical enmities for emotional appeal.
The anti-government camp in central Kiev is adorned with nationalist heroes who fought tsarist and Soviet control. On the other side, some present themselves as heirs to the Red Army, which drove Nazi occupiers from Ukraine in World War Two.
Mainstream leaders play down the ethnic divide and say they want good relations with both Russia and the West.
Yanukovich's main opponents, whose leaders won assurances of support from U.S. and EU officials in Germany at the weekend, are pushing for an immediate change in the political system, as well as for a revival of the EU free trade deal.
Arseny Yatsenyuk, parliamentary leader of the biggest opposition party, Batkivshchyna (Fatherland), told a meeting on Monday of parliament's agenda-setting committee that his bloc was ready to vote on a constitutional bill as early as Tuesday.
Party allegiances in the single-chamber legislature have been fluid and it is unclear how far the opposition can rally a majority over Yanukovich's Party of the Regions and its allies.
The bill would restore the constitution to a version enacted in 2004 during Ukraine's post-Soviet "Orange Revolution".
Yatsenyuk, who last week turned down an offer from Yanukovich to become prime minister, said restoring the 2004 constitution would "cancel the dictatorial authority of the president" and give parliament the power to form governments.
On Sunday, the government bowed to intense Western pressure and let an opposition activist fly to the European Union for treatment after his abduction, torture and then attempted arrest by police last week fuelled outrage among protesters.
Dmytro Bulatov, 35, whose bloodied face and account of being "crucified" during a week in the hands of mysterious kidnappers has dominated opposition media, is now in Lithuania. (Additional reporting by Pavel Polityuk; Writing by Richard Balmforth and Alastair Macdonald; Editing by Giles Elgood)