By David Brunnstrom

BRUSSELS, Dec 5 (Reuters) - The European Union should seize on Barack Obama's election as U.S. president as a chance to press for a more collaborative, U.N.-led approach to tackling world crises, an EU security review will say next week.

"At a global level, Europe must lead a renewal of the multilateral order...we have a unique moment to renew multilateralism, working with the United States and with our partners around the world," a draft of the review says.

The United Nations should be at the "apex" of such an approach, it adds.

The document is an update of an EU security strategy agreed in 2003 in a bid to heal deep splits within the bloc over the U.S.-led invasion of Iraq.

Many EU states were alarmed by the unilateral approach pursued by U.S. President George W. Bush, especially in his first term, and have been heartened by the prospect of Obama, who opposed the Iraq war and has favoured multilateralism.

The security review highlights growing threats posed by nuclear proliferation, cyber crime and disruption to energy supplies. It will stress the need to remain engaged with Russia and to fully involve emerging global powers such as China and India in international decision-making.

"Europe faces increasingly complex threats and challenges," said a draft summary to be presented to EU foreign ministers on Monday before endorsement by EU leaders at a Dec. 11-12 summit.

"Globalisation has...made threats more complex and interconnected," it says. "(It) is accelerating shifts in power and is exposing differences in values. Recent financial turmoil has shaken the developed and the developing world alike."

"Terrorism and organised crime have evolved with a new menace," the paper adds. "The Iranian nuclear programme has significantly advanced, representing a danger for stability in the region and the whole non-proliferation system."

"MORE CAPABLE, MORE COHERENT AND MORE ACTIVE"

For the EU to lead a renewal of multilateralism, it was necessary for it to be "more capable, more coherent and more active" in world affairs.

The paper highlights progress in developing a common European security policy, with more than 20 missions deployed in response to crises ranging from Aceh to Chad.

"But there is no room for complacency," it says. "To ensure our security and meet the expectations of our citizens, we must be ready to shape events. That means becoming more strategic in our thinking, and more effective and visible around the world."

A senior EU official said the review would stress the need for the EU to strengthen its ability to deploy missions by making up shortfalls in equipment such as transport aircraft and helicopters and improved training.

It will also stress the need to build on relations with eastern and southern neighbours and to cooperate with Russia, despite concerns about Moscow's war with Georgia in August.

"We need to engage Russia; we need to tie Russia to a rules-based system on the economic and political level," the official said. "There is no other alternative; indignation is not a policy. The solution can only be engagement."

(Editing by Mark Trevelyan)

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