By Steve Holland and Roberta Rampton

WASHINGTON (Reuters) - Ten days after President Barack Obama said he had authorized U.S. air strikes against Islamic State targets in Syria, the White House gave no sign on Friday that attacks were imminent as he prepared to meet world leaders at the United Nations.

At a White House briefing, national security adviser Susan Rice was vague as to when the new air campaign might begin in Syria, and whether Obama would in fact sign off on any final attack plan developed by the Pentagon.

"I don't think it would be appropriate or wise for me to telegraph from the podium exactly when that will occur, and what steps may need to be taken before that is to occur," Rice told reporters at the White House.

She said any attacks in Syria would be "at a time and a place of our own choosing" and that "when and how we choose to do that will be an operational decision."

Her comments underline mounting questions over when the United States will expand its air campaign against Islamic State into Syria from neighboring Iraq after Obama laid out guidelines for strikes aimed at denying the militants a safe haven in either country.

Obama said on Sept. 10 that he had authorized air strikes in Syria and has worked to prepare war-weary Americans for that eventuality.

On Wednesday, Obama visited the U.S. Central Command military headquarters in Tampa, Florida, and reviewed contingency plans developed by military commanders, declaring afterward that they were "very thorough," said White House spokesman Josh Earnest.

ATTACK PLAN SEEN UNDER DEVELOPMENT

Defense Secretary Chuck Hagel left the impression in congressional testimony on Thursday that Obama still had to decide on the final attack plan.

"The president has not yet approved its finality," he told the House of Representatives Armed Services Committee.

At a Democratic National Committee event on Friday, Obama repeated U.S. determination to act.

"America is leading the coalition that will degrade and ultimately destroy the terrorist group known as ISIL," Obama said, using an acronym for Islamic State. "And as Americans we welcome these responsibilities. We don't shy away from them."

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Other events this week suggest a war plan that is still being developed.

U.S. officials said it would take months to arm and train moderate Syrian rebels after Congress approved Obama's request for $500 million to pay for the project.

They insisted, however, that going ahead with air strikes in Syria did not hinge on having the rebels trained first.

There has also been a highly public debate over whether Americans could get involved in ground combat in Iraq.

Obama has already ordered some 1,600 U.S. troops into Iraq. That number might increase at some point, if needed, General Raymond Odierno, chief of staff of the Army, said on Friday.

"I don't think there's a rush ... to have lots of people in there now," Odierno told reporters, calling 1,600 "a good start."

Marine General Martin Dempsey, chairman of the U.S. military's Joint Chiefs of Staff, said Obama will decide on a case-by-case basis whether small groups of American advisers would go into battle with Iraqi troops.

The White House swiftly responded that Obama would not permit American combat troops to go into battle in Iraq, but that some advisers could go to forward positions to help call in air strikes.

Obama will give a speech at the U.N. General Assembly on Wednesday to make the case again for world action against Islamic State.

He will chair a meeting with global leaders to develop a strategy for preventing foreign fighters who have sworn allegiance to Islamic State from returning to their home countries to launch attacks against civilians.

(Additional reporting by Phil Stewart; Editing by Jason Szep and Andre Grenon)