* 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
* Ukraine offers autonomy, Russian language guarantees
By Pavel Polityuk and Aleksandar Vasovic
KIEV/DONETSK, Ukraine, April 19 (Reuters) - The Ukrainian government said it will not attack pro-Russian separatists over the Easter weekend as its U.S. ally threatened Moscow with new sanctions if it fails to persuade the militants to surrender.
The Kremlin denies having control over gunmen who want their eastern regions to follow Crimea in being annexed by Russia. Moscow scolded Washington for treating Russia like a "guilty schoolboy" following their agreement in Geneva on Thursday that Ukrainian militants should disarm and vacate occupied buildings.
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 government initiatives to defuse the crisis issued late on Friday. A spokeswoman for the SBU state security service said on Saturday the suspension was "linked to the implementation of the Geneva agreement and the Easter holidays".
"The anti-terrorist operation was put on hold for the Easter time and we will be not using force against them at this moment," Foreign Minister Andriy Deshchytsia was quoted on Saturday as saying by Britain's BBC.
On Friday he warned the militants that "more concrete actions" could be taken next week if they failed to start surrendering to international peace monitors.
Deshchytsia met officials in Kiev on Saturday from the OSCE, a European security body that includes both NATO members and Russia. The OSCE will oversee implementation of the Geneva accord, under which Russia, Ukraine, the United States and European Union agreed to a process of disarmament and an end to occupations as part of wider programme to defuse the gravest East-West crisis since the end of the Cold War.
A senior OSCE official will head to Donetsk, the biggest city of the Russian-speaking east, later on Saturday. OSCE officials said there was so far no indication from militants there that they had the "political will" to give up.
On Friday, separatist leaders said Russia's signature on the Geneva deal was not binding on them. Moscow denies Western assertions that it is controlling the Ukrainian activists.
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."
Russia denies preparing to invade, despite massing thousands of troops on the frontier. On Saturday a Kremlin spokesman said troops on the border were there only as a precaution against any spillover of violence, not to interfere in Ukraine.
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.
In a transcript of an interview to be broadcast later by Rossiya television, Putin spoke of having a "very good" personal relationship with former Norwegian prime minister Jens Stoltenberg, who will succeed Anders Fogh Rasmussen as secretary-general of the Western defence alliance in October.
"But let's see how he will develop relations in his new capacity," Putin added, repeating his low opinion of Rasmussen, a former Danish premier who angered the Kremlin.
Putin did not spell out what he hoped the West would do.
Moscow says its interest is only to protect its borders and Russian-speakers in Ukraine from "fascists" and others who overthrew the President Viktor Yanukovich after he sparked months of protests by rejecting closer ties with the EU.
The United States and European Union, which support the new authorities in Kiev, 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 obviously we've been very clear that 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.
U.S. Secretary of State John Kerry called Russian Foreign Minister Sergei Lavrov and urged "full and immediate compliance" with the Geneva agreement. The State Department said Kerry also called Ukrainian Prime Minister Arseny Yatseniuk and praised him for measures his side had taken so far.
One step the Ukrainian government has said it did not plan to take is remove the barricaded camp on Kiev's Independence Square, known as Maidan, which played a crucial role in bringing down Yanukovich and where activists say they will remain until legitimate presidential election due May 25.
Foreign Minister Deshchytsia said the Maidan was not an "illegal" occupation and so unaffected by the Geneva deal.
A Russian diplomat said that was a misreading of the accord.
The self-declared leader of all the eastern separatists said he did not consider his forces to be bound by Russia's signature in Geneva. Denis Pushilin, head of the self-declared Donetsk People's Republic, said Lavrov "did not sign anything for us".
On Saturday, he renewed his call for a referendum giving the eastern areas sovereign power to choose possible annexation.
But an opinion poll published by a Kiev institute found only about a third of people in the easternmost regions of Donetsk and Luhansk saying they would vote for rule by Moscow - though more than two thirds regard the new Kiev leadership as having illegally usurped the Kremlin-backed president in February.
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.
The Kremlin denies any ambition to take territory and many analysts believe it is principally seeking to influence events in Ukraine to 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. (Additional reporting by Thomas Grove in Slaviansk, Ukraine, Pavel Polityuk and Alastair Macdonald in Kiev, Vladimir Soldatkin and Christian Lowe in Moscow and David Brunnstrom in Washington; Writing by Alastair Macdonald; Editing by Peter Graff)