* Poroshenko takes uncompromising line on Crimea, EU
* Seeks peace in east, offers corridor for fighters to leave
* Scornful response from pro-Russian separatists
* Putin orders tighter controls at Russia-Ukraine border (Updates with Putin order, Russian foreign ministry statement, Kerry)
By Richard Balmforth
KIEV, June 7 (Reuters) - Ukraine's new president Petro Poroshenko said his country would never give up Crimea and would not compromise on its path towards closer ties with Europe, spelling out a defiant message to Russia in his inaugural speech on Saturday.
The 48-year-old billionaire took the oath of office before parliament, buoyed by Western support but facing a crisis in relations with Russia as a separatist uprising seethes in the east of his country.
Russia annexed the Crimean peninsula in March, weeks after street protests ousted Poroshenko's pro-Moscow predecessor Viktor Yanukovich, in a move that has provoked the deepest crisis in relations with the West since the Cold War.
"Citizens of Ukraine will never enjoy the beauty of peace unless we settle our relations with Russia. Russia occupied Crimea, which was, is, and will be, Ukrainian soil," Poroshenko said in a speech that drew a standing ovation.
He said he had delivered that message to Russian President Vladimir Putin when the two met on Friday at a World War Two anniversary ceremony in France.
There is no prospect of Russia reversing its takeover of Crimea, but in what could be a positive signal from Moscow, Russian news agencies reported Putin had ordered the Federal Security Service to strengthen protection of the border with Ukraine and prevent people crossing illegally.
The move was potentially significant because Ukraine and Western governments have been pressing Moscow to stop what they say is a flow of Russian arms and fighters into eastern Ukraine.
Russia denies it is backing the uprising but journalists have encountered Russian nationals among the separatist ranks.
Poroshenko, who earned his fortune as a confectionery entrepreneur and is known locally as the "Chocolate King", said he intended to sign the economic part of an association deal with the European Union as a step towards full membership.
That idea is anathema to Moscow, which wants to keep Ukraine in its own post-Soviet sphere of influence.
His voice swelling with emotion, Poroshenko stressed the need for a united Ukraine and the importance of ending the conflict that threatens to further split the country of 45 million people. He said it would not become a looser federalised state, as advocated by Russia.
"There can be no trade-off about Crimea and about the European choice and about the governmental system. All other things can be negotiated and discussed at the negotiation table. Any attempts at internal or external enslavement of Ukraine will meet with resolute resistance," he said.
Since Poroshenko's election, government forces have stepped up their operations against the separatists who want to split with Kiev and join Russia. The rebels have fought back, turning parts of the Russian-speaking east into a war zone.
Poroshenko offered to provide a safe corridor for Russian fighters to go home. "Please, lay down the guns and I guarantee immunity to all those who don't have bloodshed on their hands."
Switching from Ukrainian into Russian, he promised to visit the east with guarantees of Russian-language rights and proposals for decentralisation that would give its regions a bigger say in running their own affairs.
But a scornful response from the rebels, who have declared their own "people's republics", spelled out the scale of the separatist challenge facing him.
"What they (Kiev's leaders) really want is one-sided disarmament and for us to surrender. That will never happen in the Donetsk People's Republic," a top separatist official, Fyodor Berezin, said by telephone from Donetsk, an industrial hub where rebels have occupied strategic points.
"As long as Ukrainian troops are on our soil, I can see that all Poroshenko wants is subjugation. The fight will continue."
AT ODDS WITH MOSCOW
Poroshenko won a landslide election on May 25 after promising to bridge the east-west divide that has split the country and thrust it into a battle for survival.
Many Ukrainians hope the election of the former government minister, who is married with four children, will bring an end to the most tumultuous period in their post-Soviet history.
More than 100 people were shot dead by police in Kiev by police in the street protests that eventually brought Yanukovich down. In the east, scores of people, including separatist fighters and government forces, have been killed since April.
The uprising is not the only challenge facing Poroshenko, who inherits a country on the verge of bankruptcy and rated by watchdogs as one of the most corrupt and ill-governed in Europe.
Kiev is also at odds with Moscow over Russian gas. Russia is threatening to cut supplies as early as next week unless Ukraine settles its debt, the amount of which is disputed.
Poroshenko's speech drew an ovation from guests at a ceremony attended by Lithuanian President Dalia Grybauskaite, U.S. Vice President Joe Biden and senior EU officials.
Cheering crowds later greeted him on a walk in blazing sunshine on the square in front of Kiev's St Sophia's Cathedral, which was decked out with the blue and yellow national flags.
On a visit to France, U.S. Secretary of State John Kerry said Washington hoped for a reduction in Russia-Ukraine tensions in the next few days, including a possible ceasefire.
Russia's foreign ministry, in its first comments after Poroshenko's swearing-in, acknowledged his inauguration but did not comment on his speech, calling instead for the release of two Russian journalists detained in Ukraine.
But reaction was hostile in eastern Ukraine, where government forces shelled rebel positions in Slaviansk and manned checkpoints on roads into the city. In another eastern city, Luhansk, separatist leader Valery Bolotov was emphatic in his rejection of Poroshenko and Ukrainian rule.
"The Ukrainians have made their choice and they must live with it. As for our republic, we have no diplomatic relations with Ukraine," he told journalists, wearing combat fatigues in a conference room hung with crystal chandeliers.
"Today Ukraine got a new president and now the blood of our people and of Ukrainians will lie on his conscience." (Additional reporting by Lidia Kelly in Moscow, Thomas Grove in Slaviansk and Alissa de Carbonnel in Luhansk; Writing by Mark Trevelyan; Editing by David Holmes)