The Ukrainian President Petro Poroshenko has said his country would never give up Crimea and would not compromise on its path towards closer ties with Europe.

He used his inaugural speech this morning to send a defiant message to Russia.

The 48-year-old billionaire took the oath of office before parliament, buoyed by Western support.

However, he faces an immediate 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 Mr Poroshenko's pro-Moscow predecessor.

The annexation has provoked the deepest crisis in relations with the West since the Cold War.

Meanwhile, Russian President Vladimir Putin has ordered the border service to reinforce the state border with Ukraine, the Kremlin press service told Russian news agencies.

Mr Putin issued the order for border guards to take all necessary measures to prevent illegal crossings.

In this morning's speech, Mr Poroshenko said: "Citizens of Ukraine will never enjoy the beauty of peace unless we settle down our relations with Russia.

"Russia occupied Crimea, which was, is, and will be Ukrainian soil," he said in a speech that was greeted with a standing ovation.

He had told this to Mr Putin when the two met yesterday at a World War II anniversary ceremony in France, he said.

Mr Poroshenko, known locally as the Chocolate King, said he intended very soon to sign the economic part of an association agreement with the EU, as a first step towards full membership.

This idea is anathema to Moscow, which wants to keep Ukraine in its own post-Soviet sphere of influence.

His voice swelling with emotion, Mr 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.

Cheering crowds later greeted him on a walkabout on the square in front of Kiev's St Sophia's Cathedral.

Since Mr Poroshenko's election, government forces have begun an intensified campaign against the separatist rebels in eastern Ukraine, who want to split with Kiev and become part of Russia.

The rebels have fought back, turning parts of the east into a war zone.

Yesterday, they shot down a Ukrainian army plane and killed a member of the interior ministry's special forces in the separatist stronghold of Slavyansk, where residents said shelling continued all day.

Mr Poroshenko has urged the pro-Moscow separatists to lay down their arms and said he would guarantee a safe corridor for Russian fighters to go home.

US Secretary of State John Kerry has voiced hope that there would be a breakthrough on ending the Ukraine crisis, enabling Washington to avoid imposing new sanctions against Russia.