By David Alexander

MUNICH (Reuters) - Defense Secretary Leon Panetta reassured European allies on Saturday that Washington remains committed to their security despite an austerity drive, pledging greater support for a NATO rapid-action force even as he cuts U.S. troops in the region.

Panetta said the U.S. Army would still have about 37,000 soldiers in Europe even after it withdraws two of its four combat brigades -- about 7,000 soldiers - as part of efforts to trim $487 billion from the defense budget over the next decade.

"Our military footprint in Europe will remain larger than in any other region of the world," Panetta told a Munich security conference.

"That's not only because the peace and prosperity of Europe is critically important to the United States, but because Europe remains our security partner of choice for military operations and diplomacy around the world. We saw that in Libya last year, and we see it in Afghanistan every day," he said.

The United States has about 80,000 military personnel in Europe when Air Force, Navy and other troops are included. There are 28 U.S. military bases - 16 Army, 8 Air Force and 4 Navy.

The U.S. decision to cut its troop presence in Europe has raised concerns among the North Atlantic allies about waning support for its treaty commitment to mutual security and whether NATO forces would be able to train together enough to be able to conduct joint wartime operations.

Panetta has said the United States would rotate U.S.-based soldiers to Europe for training on a regular basis. On Saturday he pledged to commit one U.S.-based brigade as Washington's contribution to the NATO Response Force.

"The NRF was designed to be an agile, rapidly deployable, multinational force that can respond to crises when and where necessary," he said. "The United States has endorsed the NRF but has not made a tangible contribution due to the demands of the wars - until now."

U.S. lawmakers have been critical of Europe for low levels of defense spending and have pressed for the withdrawal of American forces, saying it was time for the continent to shoulder more of the expense of defending itself.

But with all NATO allies facing budget constraints and falling defense spending, Panetta urged nations to work together to identify key military capabilities they would need over the next decade and cooperate to ensure they are maintained.

"We must all continue to invest in national defense and in the shared responsibility and capabilities of NATO in order to best manage the security challenges of the future," he said.

(Reporting By David Alexander; Editing by Peter Graff)