By Laura Smith-Spark and Phil Black
DONETSK, Ukraine (CNN) -- The self-declared leader of pro-Russian separatists in the eastern Ukraine city of Donetsk on Friday defied an international deal for protesters to vacate seized buildings and lay down their arms.
The deal was agreed to by Russia, Ukraine and the West.
Thrashed out Thursday in Geneva, Switzerland, by Russian Foreign Minister Sergey Lavrov and his Ukrainian, U.S. and European Union counterparts, it is intended to be the first step toward easing the crisis in Ukraine.
But its proof will be in whether words translate into action on the ground. In the city of Donetsk, at least, the first signs were not promising.
"Lavrov did not sign anything for us, he signed on behalf of the Russian Federation," Denis Pushilin, head of the self-declared Donetsk People's Republic, told reporters in the city.
The demonstrators will only leave occupied buildings in eastern Ukraine if the country's interim government in Kiev resigns, he said.
Pushilin said this week he wants a referendum by May 11 to ask residents whether they want sovereignty. It's a step that may be popular with those who view Ukraine's interim authorities, who took power after President Viktor Yanukovych's ouster in February, as illegitimate.
The joint statement agreed upon in Geneva calls for all illegal armed groups to be disarmed, all illegally seized buildings to be returned to their legitimate owners and all occupied public spaces to be vacated.
It also promises amnesty for protesters who leave buildings and give up their weapons, apart from those convicted of capital crimes.
But the key to this agreement is whether Russia can and does use its influence to persuade protesters to comply.
Acting Ukrainian Foreign Minister Andriy Deshchytsia told reporters in Kiev on Friday that Russia still must prove its intentions in Ukraine are sincere.
"I don't know the Russian intentions but Minister Lavrov did promise that they want to de-escalate, so we will see in a few days if it was (a) sincere promise and sincere participation," he said.
Deshchytsia said the government's "anti-terrorist operation" against the pro-Russian protesters who have taken control of key sites will continue, but that its intensity will "depend on the practical implementation" of the pact.
All sides agreed Thursday to ask for monitors from the Organization for Security and Cooperation in Europe, which has a mission in Ukraine, to help implement the measures.
But with tensions still high and Ukraine's security forces in an uneasy standoff with the armed protesters who have seized swaths of eastern Ukraine, the challenges of restoring calm remain great.
Even as he announced the pact Thursday, U.S. Secretary of State John Kerry stressed that the proof of the agreement would be in its swift implementation on the ground.
"The job will not be done until these principles are implemented and are followed up on," he said.
Kerry warned that Russia could face "further costs" if the situation does not de-escalate in line with the concrete steps set out in the statement. Ukraine's leaders must also play their part in calming the situation, he said.
Caution, skepticism greet deal
A few hours later, U.S. President Barack Obama also voiced his skepticism.
"I don't think we can be sure of anything at this point," Obama said at a press conference Thursday.
The President also said the United States and its allies "have to be prepared -- potentially -- to respond," to continued efforts by Russia to interfere in southern and eastern Ukraine.
"I think there is the possibility, the prospect, that diplomacy may de-escalate the situation," he said. But he added, "We're not going to know whether there is follow-through on these statements for several days."
In an interview with CNN, Ukrainian Prime Minister Arseniy Yatsenyuk also said he was happy but cautious after the Geneva talks.
Yatsenyuk said he was willing to grant more autonomy to eastern Ukraine to defuse tensions.
Lavrov, the Russian foreign minister who took part in the Geneva talks, highlighted the need to protect ethnic Russians from discrimination and include all parties in Ukraine in a national dialogue on constitutional reform.
Obama: Russia must take concrete action
At the White House, Obama stressed he has emphasized to Russian President Vladimir Putin that the United States will continue to uphold the basic principles of sovereignty of all countries.
However, he said that military options are still not on the table "because this is not a situation that would be amendable to a clear military solution."
In calls with German Chancellor Angela Merkel and UK Prime Minister David Cameron, Obama again urged Russia to "take immediate, concrete actions to de-escalate the situation in eastern Ukraine, including by using its influence over the irregular forces in eastern Ukraine to get them to lay down their arms and leave the buildings they have seized."
U.N. Secretary-General Ban Ki-moon welcomed negotiations, while stressing the situation in Ukraine remains "extremely volatile."
Ban "expects all sides, moving forward, to show their serious intention to continue to engage, in a good-faith effort, and to implement the steps laid out in the Geneva Statement, which will contribute to a lasting solution to this crisis," a U.N. statement read.
Putin: Intervention still an option
The emergency talks in Geneva were called amid the spiraling crisis in Ukraine that has seen East-West relations at their most strained since the end of the Cold War.
The tensions erupted into violence Thursday in the southeastern city of Mariupol, where a gang of 300 attacked a Ukrainian military base, leading to gunfire between the two sides.
Even as the negotiations in Geneva were under way, Putin made clear in his annual televised call-in session with the Russian people that military intervention in Ukraine remains an option.
Moscow denies it has any intention of invading -- but says it reserves the right to protect Russian speakers in eastern Ukraine. It has warned in the past week that Ukraine is "on the brink of a civil war."
NATO says Russia currently has some 40,000 troops assembled near Ukraine's eastern border. Russia says they are merely conducting military exercises.
In his remarks, Putin also said Russian forces had been active in Ukraine's Crimea region to support local defense forces, the first time he has acknowledged the deployment of Russian troops on the Black Sea peninsula.
Russia annexed Crimea last month following a controversial referendum in which almost all those who voted opted to join Russia. The peninsula has a majority Russian-speaking population.
Amid concerns over alleged Russian interference in eastern Ukraine, the authorities in Kiev said Thursday they were tightening border controls to limit the entry of Russian men ages 16 to 60.
CNN's Phil Black reported from Donetsk and Laura Smith-Spark wrote and reported from London. CNN's Frederik Pleitgen, Kellie Morgan and journalist Azad Safarov, all in Kiev, contributed to this report, as did Tim Lister in Donetsk.
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