* Four-way talks end with call for end to Ukraine violence
* On ground, pro-Russian gunmen holding their positions
* Kiev's Maidan says it won't budge either
* Obama says talks offer hope that diplomacy can work
* Deal did not mention Russia's annexation of Crimea (Adds constitutional offer from Kiev, Russian foreign ministry comments)
By Thomas Grove and Aleksandar Vasovic
SLAVIANSK/DONETSK, Ukraine, April 18 (Reuters) - Armed pro-Russian separatists in eastern Ukraine said on Friday they were not bound by an international deal ordering them to disarm and would not move out of public buildings they have seized until the Kiev government stepped down.
The agreement, brokered by the United States, Russia, Ukraine and the European Union in Geneva on Thursday, seemed to be the best hope of defusing a stand-off in Ukraine that has dragged East-West relations to their lowest level since the Cold War.
Ukraine's acting president and prime minister offered some of their strongest pledges yet to strengthen constitutional rights to use the Russian language to try and defuse the protests but Kiev also said its efforts to root out the separatists would continue.
The Geneva agreement requires all illegal armed groups to disarm and end occupations of public buildings, streets and squares, but with the separatists staying put in the east and Ukrainian nationalist protesters showing no sign of leaving their - unarmed - camps in the capital's Maidan Square, it was not clear that either side would be willing to move first.
Enacting the agreement on the ground will be difficult, because of the deep mistrust between the pro-Russian groups and the Western-backed government in Kiev. This week has already seen several people killed in violent clashes.
The fact a deal was reached in Geneva came as a surprise, and it was not clear what had happened behind the scenes to persuade the Kremlin, which had shown little sign of compromise, to join calls on the militias to disarm. It rejects Ukrainian and Western accusations of orchestrating the gunmen.
Russian President Vladimir Putin overturned decades of post-Cold War diplomacy last month by declaring Russia had a right to intervene in neighbouring countries and by annexing Ukraine's Black Sea peninsula of Crimea.
That move followed the overthrow of Ukraine's pro-Moscow president Viktor Yanukovich after months of street protests prompted by his rejection of a trade deal with the EU.
In Slaviansk, a city that has become a flashpoint in the crisis after men with Kalashnikovs took control last weekend, leaders of the pro-Russian groups met inside one of the seized buildings to decide how to respond to the Geneva agreement.
Anatoly, one of the armed separatists who have taken over police headquarters, said: "We are not leaving the building, regardless of what statements are made, because we know what is the real situation in the country and we will not leave until our commander tells us to."
Two Ukrainian military aircraft circled Slaviansk several times on Friday. In front of the mayor's office, men armed with automatic rifles peered over sandbags that had been piled higher overnight. Separatists remained in control of the city's main streets, searching cars at checkpoints around the city.
In a joint televised address, acting President Oleksander Turchinov and Prime Minister Arseny Yatseniuk called for national unity, urged people to refrain from violence and said they would support constitutional change, decentralising more power to local councils, including over their official language - a key demand of Russian-speakers.
Kiev also said the government was preparing a law that would give the separatists an amnesty if they backed down.
The self-declared leader of all the region's separatists said he did not consider his men to be bound by the agreement.
Denis Pushilin, head of the self-declared Donetsk People's Republic, told journalists in Donetsk, the regional capital, that Russian Foreign Minister Sergei Lavrov "did not sign anything for us; he signed on behalf of the Russian Federation".
First, he said, the prime minister and acting president who took power in February should quit their offices, as they took them over "illegally".
But Alexei, another separatist in Slaviansk, acknowledged that the Geneva talks had changed the situation: "It turns out Vova doesn't love us as much as we thought," he said, using a diminutive term for Putin, who is viewed by many of the separatist militias as their champion and protector.
In the capital, Kiev, people on the Maidan, the local name given to Independence Square, which was the centre of protests that eventually toppled Yanukovich, said the barricades would not come down until after the May 25 presidential election.
"People will not leave the Maidan. The people gave their word to stay until the presidential elections so that nobody will be able to rig the result. Then after the election we'll go of our own accord," said 56-year-old Viktor Palamaryuk from the western town of Chernivtsi.
"Nobody will take down our tents and barricades," said 34-year-old Volodymyr Shevchenko from the southern Kherson region. "If the authorities try to do that by force, thousands and thousands of people will come on to the Maidan and stop them."
Right Sector, a far-right nationalist group whose violent street tactics in support of the Maidan helped bring down Yanukovich in February, saw the Geneva accord as being directed only at pro-Russian separatists in the east.
"We don't have any illegal weapons, and so the call to disarm will not apply to us," said Right Sector spokesman Artem Skoropadsky. "We, the vanguard of the Ukrainian revolution, should not be compared to outright gangsters."
President Barack Obama said the meeting in Geneva between Russia, Ukraine and Western powers was promising but that the United States and its allies were prepared to impose more sanctions on Russia if the situation fails to improve.
"There is the possibility, the prospect, that diplomacy may de-escalate the situation," Obama told reporters.
"The question now becomes, will in fact they use the influence they've exerted in a disruptive way to restore some order so that Ukrainians can carry out an election and move forward with the decentralisation reforms that they've proposed," he said at the White House.
Ukraine's government promises to devolve power to the regions and protect people's rights, notably in the east, to use the Russian language in public life. But it rejects calls for a federal structure that it says could lead to permanent Russian interference in the east and eventually break up the country.
U.S. Secretary of State John Kerry said in Geneva that if by the end of the weekend there were no signs that pro-Russian groups were pulling back, there would be costs for Moscow, a reference to further EU and U.S. sanctions.
Russia said the threat of new sanctions against Moscow by Washington was "completely unacceptable".
The Foreign Ministry accused U.S. officials of seeking to whitewash what it said was the use of force by the Ukrainian government against protesters in the country's mainly Russian-speaking eastern provinces.
The Geneva deal did not mention Russia's annexation of Crimea, though Western diplomats said they remained firm that Russia acted illegally and denied they had dropped the issue.
The fact the agreement did not address Crimea could put pressure on Ukraine's interim government from its own supporters, who are adamant that everything should be done to bring the peninsula back under Kiev's control.
The United States and EU have so far imposed visa bans and asset freezes on a small number of Russians, a response that Moscow has openly mocked. Western states say they are now contemplating measures that could hurt Russia's economy more broadly.
Some EU nations are reluctant to press ahead with more sanctions, fearing that could provoke Russia further or end up hurting their own economies, which rely on Russian gas.
The Moscow-led South Stream undersea gas pipeline project to bring gas to southeast Europe is still under way, and Russia has been discussing its implementation with Europe, Russian Energy Minister Alexander Novak said on Friday.
He also said cooperation between Russian companies and international oil and gas majors was continuing despite Western sanctions against Moscow over Ukraine.
Royal Dutch Shell Chief Executive Ben van Beurden said he had told Putin at a meeting on Friday that the company was committed to expansion in Russia, and plans to expand Russia's only liquefied natural gas (LNG) plant with Russian partner Gazprom.
Pro-Russian militants control buildings in about 10 towns in eastern Ukraine after launching their operation on April 6.
In Luhansk, a militia member called Andrei said his group had no plans to withdraw: "Everything on the ground is the same as it was yesterday and the day before and the day before that. We're not leaving."
Seeking to reassure its eastern allies, NATO announced it was sending warships to the Baltic, while the United States approved more non-lethal military support for Ukraine.
Speaking on Russian television before the Geneva agreement, Putin accused the authorities in Kiev of plunging the country into an "abyss".
Kiev fears he will use any violence as a pretext to launch an invasion of eastern Ukraine by Russian forces. (Additional reporting by Stephanie Nebehay, Tom Miles, Arshad Mohammed and Catherine Koppel in Geneva, and Alexei Anishchuk in Moscow; Writing by Christian Lowe and Richard Balmforth; Editing by Anna Willard, Alastair Macdonald and Will Waterman)