* Three killed near rebel-held Slaviansk
* Russia, Kiev question each other's compliance with peace accord
* Washington says more sanctions on Russia if no progress
An agreement reached last week to avert wider conflict in Ukraine was faltering as the new week began, with pro-Moscow separatist gunmen showing no sign of surrendering government buildings they have seized.
U.S. and European officials say they will hold Moscow responsible and impose new economic sanctions if the separatists do not clear out of government buildings they have occupied across swathes of eastern Ukraine over the past two weeks.
U.S. Vice President Joe Biden arrived in Kiev, where he is expected to announce a package of technical assistance. The visit is likely to be more important as a symbol of support than for any specific pledges Biden makes in public.
Russia, Ukraine, the European Union and the United States signed off on an agreement in Geneva on Thursday designed to lower tension in the worst confrontation between Russia and the West since the Cold War. The agreement calls for occupied buildings to be vacated under the auspices of envoys from the Organization for Security and Cooperation in Europe.
But no sooner had the accord been signed than both sides accused the other of breaking it, while the pro-Moscow rebels disavowed the pledge to withdraw from occupied buildings.
An OSCE mediator held his first meeting with the leader of separatists in Slaviansk, a town which rebels have turned into a heavily-fortified redoubt. Mark Etherington said he had asked the pro-Russian self-proclaimed "people's mayor" of the town, Vyacheslav Ponomaryov, whether he would comply with the Geneva agreement, but gave no hint about Ponomaryov's response.
Etherington said he had also asked about people being held in Slaviansk, including the woman who was serving as mayor until the uprising. Her fate has not been made clear.
Separatists told Reuters they would not disarm until Right Sector, a Ukrainian nationalist group based in Western Ukraine, disarms first.
"Who should surrender weapons first? Let us see Right Sector disarm first, let them make the first step and we will follow," said Yevgeny Gordik, a member of a separatist militia. "We need dialogue. This is not dialogue. It is monologue."
Russia says Right Sector members have threatened Russian speakers. Kiev and Western countries say the threat is largely invented by Russian state-run media to justify Moscow's intervention and cause alarm in Russian speaking areas.
Moscow blames Right Sector for a deadly shooting on Easter Sunday morning, when at least three people were killed at a checkpoint manned by armed separatists. Right Sector denies involvement, while Kiev said Russia provoked the violence.
Russia's Foreign Minister Sergei Lavrov described the checkpoint attack as a crime, and said Kiev was failing to implement the Geneva deal. Ukraine's Foreign Minister Andriy Deshchytsia replied that Ukraine was participating in talks led by the OSCE alongside Russian diplomats, who should have informed Lavrov of the steps Kiev was taking.
One European diplomat said the Geneva deal was a way for Putin to buy time and undermine momentum towards tougher sanctions: "Talks and compromises are just part of his tactics," said the diplomat. "He wants to have Ukraine."
SOLDIERS FREED, JOURNALIST HELD
The Slaviansk separatists released around a dozen Ukrainian soldiers in blue uniforms on Monday, without making clear the circumstances under which they had been held. Gordik said armoured vehicles that were surrendered by a column of Ukrainian paratroops last week would stay in the town.
A Ukrainian journalist captured by the separatists overnight was led out by her captors and permitted to speak to reporters. Imra Krat, 29, said she was being questioned but not mistreated. She was then blindfolded and led back inside. Ukrainian journalists say another reporter, freelancer Serhiy Lefter, 22, has been missing in Slaviansk since last week.
President Vladimir Putin overturned decades of post-Cold War diplomacy by announcing last month that Russia has the right to intervene on the territory of its neighbours to protect Russian speakers. He then seized and annexed Ukraine's Crimea peninsula.
Moscow has since massed tens of thousands of troops on the Ukrainian border, and Kiev and its Western allies say Russian agents are directing the uprising in the east, including the "green men" - heavily armed, masked gunmen in unmarked uniforms.
In his latest move, likely to be seen by the West as a further threat to the post-Cold War order, Putin signed a law on Monday making it easier for Russian speakers across the former Soviet Union to obtain Russian citizenship.
Eastern Ukraine is largely Russian speaking and many residents are deeply suspicious of the pro-European government that took power in Kiev in February when Moscow-backed President Viktor Yanukovich fled the country after mass protests.
Separatists have declared an independent "People's Republic of Donetsk" in the east's biggest province and have named themselves to official posts in towns and cities, setting up checkpoints and flying Russian flags over government buildings.
There is also some support for Ukrainian unity in the region, but pro-Kiev activists have had a lower profile since the separatists took up arms. One activist who helped organise a Ukrainian unity rally in Rubizhne, an eastern town, told Ukraine's Channel 5 television that separatists attacked it, forcing the rally to disperse. Local police said a policeman was hurt when unidentified people tried to disrupt the rally.
The Ukrainian defence ministry said gunmen on motorcycles fired on an army checkpoint between Donetsk and Slaviansk shortly after dark on Sunday. The troops returned fire, wounding one attacker and capturing two, it said.
Ukraine announced an "anti-terrorist" operation to retake rebel-held territory last week, but that modest effort largely collapsed in disarray when a column of paratroops surrendered rifle parts and some armoured vehicles to a separatist crowd.
Kiev has declared an "Easter truce", though it is far from clear it could muster any real force if it tried. The army is ill-equipped, untested and untrained for domestic operations, while the government in Kiev doubts the loyalty of the police.
The United States and European Union have imposed visa bans and asset freezes on some Russians over the annexation of Crimea, measures explicitly designed not to have wider economic impact and which have been mocked as pointless by Moscow.
Washington and Brussels both say they are working on tougher measures they will impose unless Russia's allies in eastern Ukraine back down, although building a consensus is tricky in Europe where many countries rely on Russian energy exports.
The OSCE, a European security body that includes both NATO members and Russia, has so far deployed around 100 monitors and mediators in Ukraine and expects their number to rise.
An OSCE spokesman said the mediators were visiting separatist-occupied buildings with copies of last week's Geneva accord to explain it to the people inside.
"It's a mixed experience dealing with checkpoints and so forth and there is a varying reaction to teams. There is a hardened attitude in Donetsk or Slaviansk but some other areas are more accommodating," spokesman Michael Bociurkiw said. "When teams go to smaller centres people are more willing to talk."
The OSCE mission's chief, Ertugrul Apakan, said a team of 10-12 people had gone to the region around Slaviansk on Monday after turning back on Sunday because of security concerns.
He said some occupied buildings elsewhere had been vacated. He did not provide details but said there had been progress in the port of Mariupol, scene of a deadly shooting last week when national guards repelled separatists trying to storm their base.
Details remained disputed in Sunday's shootout in Slaviansk. The separatists said armed men from Right Sector had attacked them. Right Sector denied any role, saying Russian special forces were behind the clash.