(Adds OSCE comment, colour from eastern cities)
* No moves over Easter as Ukraine works with OSCE on surrender
* Putin says West could improve relations, welcomes new NATO head
* U.S. warns of new sanctions on Russia if no resolution
* Moscow says not directing events, poll suggests most oppose annexation
By Alastair Macdonald and Aleksandar Vasovic
KIEV/DONETSK, April 19 (Reuters) - A mediator from Europe's OSCE security body headed to eastern Ukraine on Saturday seeking the surrender of pro-Russian separatists as the Kiev government declared an Easter truce following a peace accord with Moscow.
Gunmen occupying public buildings in Donetsk and other Russian-speaking border towns refuse to recognise an accord in Geneva on Thursday by which Russia, Ukraine and Kiev's U.S. and EU allies agreed that the OSCE should oversee the disarmament of militants and the evacuation of occupied facilities and streets.
The coming days may determine whether unrest following the overthrow of Ukraine's pro-Moscow president can be contained.
Russia, which annexed Crimea last month in the worst East-West crisis since the Cold War, denies running the separatists or planning to invade. Western powers threatened more economic sanctions if Moscow does not prevail on the militants to surrender.
Ertogrul Apakan, who heads the special mission in Kiev of the Organisation for Security and Cooperation in Europe, said his deputy would be in Donetsk on Saturday and meet separatist leaders by Sunday to see if they will comply with the agreement.
After a meeting in the Ukrainian capital with diplomats from the four parties to the Geneva accord, Swiss envoy Christian Schoenenberger, whose country is chair of the OSCE, said its monitors had spoken to several activists: "For the time being the political will is not there to move out," he said.
"That's the task of the monitors, to create this political will, inform the people, so eventually they will understand that the best option for them is to move out," he told reporters.
Ukrainian Foreign Minister Andriy Deshchytsia, who warned on Friday of "more concrete actions" to end the stand-off if there were no movement over the Easter weekend, said after the meeting that the senior OSCE officials and the local authorities in the east would "work out practical steps for the implementation of the Geneva agreement in the course of the next day or two".
In Donetsk, separatist leaders renewed calls for a referendum that could see Ukraine's industrial heartland annexed by Russia. A poll by an institute in Kiev, however, suggested a majority does not favour rule from Moscow, despite widespread suspicion among Russian-speakers of the new leadership in Kiev.
Ukraine's government, short of effective forces, has shown little sign of trying to recapture the dozen or so town halls, police stations and other sites seized over the past two weeks, despite proclaiming the launch of an "anti-terrorist operation".
The Foreign Ministry promised "the suspension of the active phase of the anti-terrorist operation" among a list of initiatives to defuse the crisis issued late on Friday. The SBU state security service said the suspension was "linked to the implementation of the Geneva agreement and the Easter holidays".
The government has explained its lack of visible action beyond setting up security checkpoints by a desire not to hurt civilians. That would risk provoking the intervention Russia has threatened if Russian blood is shed. But lack of resources and training also helps explain the hesitation. Ukrainian troops lost half a dozen armoured vehicles to militants last week.
"An Easter truce may show goodwill - or perhaps just Kiev's total impotence," said one of the masked men guarding the occupied headquarters of Donetsk's regional government.
"If it's impotence, then we've won. If they're getting ready to provoke us, then we will hit back with force."
Several people have been killed in violence in the past week. On Saturday, a serviceman was killed in Donetsk in what the Defence Ministry described as an accident.
After weeks of bitter mutual recriminations, Vladimir Putin held out the prospect of better relations with the West on Saturday but the Russian president made clear it would depend on concessions from his adversaries in the crisis over Ukraine.
"I think there is nothing that would hinder a normalisation and normal cooperation," he said in an interview to be broadcast by Russian state television in which he commented favourably on the appointment of a new head of NATO. "This does not depend on us. Or rather not only on us. This depends on our partners."
He did not spell out what he hoped the West would do.
President Barack Obama's officials made clear on Friday that Russia must prevail on sympathisers in Ukraine to end the sit-ins within days or face graver economic sanctions than limited measures imposed after the seizure of Crimea.
Moscow says its interest is only to protect its borders and Russian-speakers in Ukraine from "fascists" and others who overthrew President Viktor Yanukovich after he sparked months of protests by rejecting closer ties with the EU.
The United States and European Union have imposed limited sanctions on Russian officials over Crimea but are struggling to find a common approach to curbing what they see as a drive by Moscow to recover control of its former empire.
Russia has long complained NATO's extension of membership to Moscow's Cold War satellites in eastern Europe and deepening ties to ex-Soviet states like Georgia, Moldova and Ukraine is part of an aggressive policy to undermine it.
Years of Western disdain for Russia's struggles with the legacy of the communist collapse also lie behind Putin's demands - hugely popular at home - that Moscow be treated with respect. His spokesman hit back on Friday at threats of sanctions from Washington, saying it treated Russia like a "guilty schoolboy".
U.S. national security adviser Susan Rice said: "We believe that Russia has considerable influence over the actions of those who have been engaged in destabilising activities.
"If we don't see action commensurate with the commitments that Russia has made ... in Geneva ... then ... we and our European partners remain ready to impose additional costs on Russia. Those costs and sanctions could include targeting very significant sectors of the Russian economy."
Washington did not spell out what further sanctions it might place on Russia. With the EU, it has so far imposed visa bans and asset freezes on a small number of Russians, a response that Moscow has mocked. But some EU states are reluctant to do more, fearing that could provoke Russia further or end up hurting their own economies, which are heavily reliant on Russian gas.
Massive unknowns hang over the situation. Putin's ultimate goal may not be the Crimean-style annexation of Ukraine's industrial heartland, despite his comments in a major public appearance on Thursday in which he recalled that what is now eastern and southern Ukraine was the tsars' New Russia.
Many analysts believe Putin is mainly seeking to influence events in Ukraine and ensure a favourable outcome in next month's election following the loss of Russian ally Yanukovich.
That in turn raises questions of the role of Ukraine's rich business "oligarchs" in the crisis and the election.
Conspiracy theories abound in Kiev, according to which the rich and powerful may be fomenting unrest behind the scenes to further their own ends or to curry favour with Putin, who holds sway over the Russian business interests of Ukrainian tycoons.
The Ukrainian government has been at pains to show it is ready to meet the demands of people in the east for greater local autonomy and rights to use the Russian language.
With a presidential election to replace Yanukovich planned for May 25, it also needs to convince Ukrainians that 23 years of grandiose corruption and economic mismanagement under various leaders might come to end and give the state a better future.
A poll by the Kiev International Institute of Sociology for the Zerkalo Nedeli newspaper found less than a third of people in the easternmost regions of Donetsk and Luhansk would vote for rule from Moscow and less than a quarter said they supported the takeover of public buildings in their regions by armed men.
Nonetheless, fear of "fascist" Ukrainian nationalists in Kiev, and worries for employment in the mines and factories, are widespread: "I lost my job in February when all of this chaos started in Kiev," said mother-of-two Nina Nebesna, 30, as she headed in to Donetsk's stadium to watch the local soccer derby.
"Now I can't find work anywhere," she said. "I don't recognise the junta that took power in Kiev. Those boys are standing up for our rights," she said of the local militants.
Local miner, Mikhail Belogurov, 55, said a move in the Kiev parliament after Yanukovich fell to curb Russian-language rights was "really stupid" and he wanted "the authorities in Kiev to pay more attention to us". But he was sceptical of the aims of the pro-Russian separatists: "We don't know who the people in the buildings are," he said. " We don't know what they want." (Additional reporting by Alissa de Carbonnel in Donetsk, Thomas Grove in Slaviansk, Ukraine, Pavel Polityuk in Kiev and Vladimir Soldatkin and Christian Lowe in Moscow; Writing by Alastair Macdonald; Editing by Rosalind Russell)