* Obama says U.S. must do more to court investors

* U.S. global share of investment shrinks

* Embassies to focus on investment promotion

* Plan to create single point of contact for investors

By Mark Felsenthal and Elvina Nawaguna

WASHINGTON, Oct 31 (Reuters) - President Barack Obama on Thursday pledged an aggressive expansion of U.S. efforts to draw foreign investment by clearing away red tape and having U.S. diplomats court investors who want to break into the market.

"We know we can do more. We know we can do better," Obama said at a conference his administration organized that attracted business representatives from around the world.

While the United States drew $166 billion in direct investment dollars in 2012, more than any other country, the U.S. share of foreign direct investment has fallen to 17 percent from more than a third in 2000, according to the Organization for International Investment, a trade group that represents the U.S. operations of global companies.

Seeking to reverse that trend, Obama said the United States would start to coordinate efforts at the federal level to attract investment in a way it has not before. Until now, states and cities have been responsible for making pitches for business from abroad.

"As a country, we don't always make our case in a coordinated way that links our teams overseas to the right senior officials in Washington," he said. "And we're going to change that, make our advocacy more efficient, more effective, more connected."

The president's plug comes at a time of sluggish U.S. economic growth and uncertainty over the country's fiscal outlook as the president and congressional Republicans fight over cuts to government spending and how much deficit cutting is necessary to put the country on a sustainable fiscal course.

Obama said U.S. officials would seek to make it easier for foreign firms to navigate the thicket of federal, state and local requirements for doing business in the United States. He promised "a single point of contact" for interested investors.

The decline of U.S. market share of global foreign direct investment is due in part to rapid growth in emerging economies, OFII President Nancy McLernon said. But the United States has also failed to market itself aggressively and has lagged Europe in attracting investment from developing nations, she added.

Obama promised that top administration officials will play a more active role in pitching the United States as an attractive place to invest.

"Officials at the highest levels, up to and including me, are going to do even more to make the case for investing in America," he said.