By Adrian Croft

BRUSSELS (Reuters) - NATO's military power and global influence could be put at risk if allies continue to slash their defense budgets while emerging powers boost theirs, NATO's chief will warn on Thursday.

Anders Fogh Rasmussen is also expected to warn in his annual report, due out later on Thursday, that too deep defense cuts could worsen the West's economic crisis by weakening defense industries that are key drivers of innovation, jobs and exports.

Rasmussen's message will be that military power will remain essential if NATO wants to keep its people safe and retain global influence, NATO officials said.

He will urge allies to keep defense spending steady in 2013 and to spend more on the military once their economies pick up.

"He will make clear that we can't expect security challenges to just go away while we are focused on fixing our economies. In fact, just the opposite. There is a risk that challenges will get more complicated, more complex, because the world out there is so unpredictable," a NATO official, speaking on condition of anonymity, said.

The global financial crisis has forced many NATO allies into drastic measures to reduce their budget deficits, leading to sometimes sharp cuts in defense spending.

Only a handful of the 28 NATO allies - the United States, Britain and Greece - last year spent more on defense than the two percent of Gross Domestic Product target set by NATO.

Some could look to make further cuts once the NATO-led force ends combat operations in Afghanistan at the end of 2014.

Rasmussen will say in the report that NATO remains the world's most important military power, with NATO countries still accounting for more than half of global defense spending.

CAPABILITY GAP

But he will warn that defense spending among the allies is increasingly uneven, not just between North America and Europe, but also among European allies, as some cut defense spending more than others.

If this capability gap continues to grow, it could limit the allies' ability to work together and risk weakening political support for NATO in the United States.

While total defense spending by NATO members has been going down in recent years, the defense spending of new and emerging powers has been going up.

If those trends continue, NATO's military capacity and political credibility could be put at risk, Rasmussen will say.

The rise of emerging powers could create a growing gap between their capacity to act and exert influence on the international stage and NATO's ability to do so, he will say.

Rasmussen will not name any countries but China boosted military spending by 11 percent last year, continuing a near-unbroken string of double-digit rises across two decades.

Defense spending by NATO's military superpower, the United States, is set to be $633 billion this year.

That dwarfs China's official military spending, $110 billion in 2012, although many foreign experts believe Beijing's public budget undercounts its real spending on military modernization.

China's growing military influence has coincided with a more assertive diplomatic tone, evident in rows with Japan and Southeast Asia over disputed islands.

(Editing by Rosalind Russell)