Ukraine's newly elected president has pledged to retake Crimea and said he would not back down in seeking closer ties with Europe during his inaugural speech today.

The comments come in the face of a deepening crisis in relations with Russia and a violent separatist uprising that has gripped the east of the country.

Petro Poroshenko, a 48-year-old billionaire, made his address shortly after being sworn into office in front of parliament and foreign guests including US Vice President Joe Biden and senior European Union officials, according to Reuters.

"There can be no trade-off about Crimea and about the European choice and about the governmental system," Poroshenko said. "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."

Poroshenko called to " settle our relations with Russia," but said that Crimea, which was annexed by Russia this spring "was, is, and will be Ukrainian soil."

No mention was made on how Ukraine planned to reclaim the Black Sea peninsula that is home to the strategic naval base of Sevastopol.

The new leader also restated intentions to secure full Ukrainian incorporation into the EU, with the first step being to sign off on the economic component of an association agreement.

The move for closer relations with the West comes despite Russia's efforts to retain influence of Ukraine in the post-Soviet era, and Russia's repeated threats to withhold natural gas supplies from the country.

Ukraine’s border guard service released a video on June 6 which is described as showing the aftermath of a “terrorist attack” on a checkpoint in the southeast of the country on June 5.

Ukraine would not become a federalized state as Moscow has advocated, the new president said.

Instead, Poroshenko promised to call for early regional elections in the east and make bids to allocate new powers to regional governments, according to the Associated Press.

The strongly-worded speech came a day after Poroshenko and Russian President Vladimir Putin met on a D-Day anniversary ceremony in Normandy, France, where the pair engaged in possible ceasefire talks to resolve the crisis in Ukraine's majority Russian-speaking east which officials claim has killed more than 200 people so far.

Barack Obama and Vladimir Putin met informally on the sidelines of a lunch, which was attended by world leaders to mark the 70th anniversary of the D-Day landings in Normandy, on June 6.

Kiev government leaders and the West have blamed Russia for fanning the flames of the uprising by pro-Moscow rebels who want to split with Kiev and join Russia. Putin has denied the claims.

Poroshenko also pledged to bring peace to Ukraine, but made no mention of whether he would pull backs its military operation against the insurgents.

He also promised "immunity to all those who don't have bloodshed on their hands," if they lay down their weapons and offered "Russian militants" safe passage out of Ukraine.

But mere hours after the speech, Putin tightened security along the Russian-Ukraine border to control illegal crossings, according to Russian news media.

Meanwhile, pro-Russia separatists in the eastern regions of Luhansk and Donetsk that have declared themselves independent repudiated Poroshenko's speech.

"This statement doesn't concern us," the self-acknowledged prime minister of rebel group the Donetsk People's Republic, Alexander Borodai said, according to Russian media.

Ukraine Bets on "Chocolate King"

Poroshenko, who was elected on May 25 as Ukraine's fifth president, replaces interim president Oleksandr Turchynov who took over when former pro-Russia president Viktor Yanukovych fled the country in February in the face of months of citizen protests.

Leaders of the west, including US President Barack Obama, have endorsed the new presidency of the self-made confection mogul who is known in Ukraine as the "Chocolate King."

Poroshenko, who previously served as Ukraine's foreign minister for economic development, inherits a country on the brink of bankruptcy that has long been dogged by corruption and bloodshed and owes a massive but disputed natural gas debt to Russia.

Ukrainians hope their newly elected president, a husband and father of four children, will help repair damages caused by the conflict and violent that has overwhelmed the country's recent history.