By Ross Colvin and Jeff Mason

WASHINGTON (Reuters) - President Barack Obama will address Americans on the war in Afghanistan on December 1 and spell out a strategy that would see U.S. forces withdrawing within eight or nine years, the White House said on Wednesday.

Obama's spokesman, Robert Gibbs, said the president would use his prime-time speech to stress the "sheer cost" of the eight-year-old war, explain to Americans why their army was still in Afghanistan, and press Afghan President Hamid Karzai to improve governance after a fraud-tainted election.

"We are in the ninth year of our efforts in Afghanistan. The American people are going to want to know why we are here, they are going to want to know what our interests are," Gibbs said.

Obama has spent the past three months reviewing the U.S. strategy in Afghanistan, where a resurgent Taliban has driven violence to its highest levels since U.S. forces invaded in 2001 to oust the Islamists for harboring al Qaeda leaders responsible for the September 11 attacks on the United States.

The president has drawn fire from Republican critics for the time he has taken to reach a decision, but the White House has countered saying the former Bush administration neglected Afghanistan and allowed the security situation to deteriorate.

Obama's address to the nation at 8 p.m. EST on December 1 from the West Point military academy in New York state will mark the end of a long process of deliberation that was characterized by a slow drip of leaks about the various options he was considering.

Angered by the leaks, which some analysts saw as an attempt by some in the administration to influence the president's thinking, Obama threatened to make them a firing offense.

NOT OPEN-ENDED

Officials speaking on condition of anonymity expect Obama to announce an increase of about 30,000 troops in Afghanistan. There are currently about 110,000 foreign troops there, including 68,000 U.S. soldiers.

His top commander in Afghanistan, General Stanley McChrystal, has asked for 40,000 additional troops.

Gibbs said Obama would emphasize that the U.S. involvement in Afghanistan was not open-ended, but he declined to say whether the president would give Americans a specific timetable for the withdrawal of U.S. troops.

But, he added: "We are in year nine of our efforts in Afghanistan. We are not going to be there another eight or nine years.

"Our time there will be limited and that is important for people to understand," he said.

Obama's emphasis on a way out will please fellow Democrats who control the U.S. Congress and who face potentially difficult mid-term elections in November 2010, but Republicans will likely see it as evidence he is soft on security.

Gibbs said the sheer financial cost of the conflict -- which reached $6.7 billion in June alone -- was a major factor in Obama's determination to end the war.

"It is very, very, very expensive," Gibbs said.

The White House has estimated that it will cost $1 million per year for each additional soldier sent to Afghanistan. With the U.S. deficit hitting $1.4 trillion and fueling Americans' concerns about high government spending, sending more troops to Afghanistan could be a politically risky move for Obama.

In his speech, Obama will again press Karzai to improve the performance of his corruption-plagued government. Karzai's legitimacy was tarnished after a fraud-riddled election in August that saw millions of ballots favoring him thrown out.

"As the president has told President Karzai, there has to be a new chapter in Afghan governance and that is something the president will talk about on Tuesday," Gibbs said.

Obama will brief NATO allies and members of Congress on his plans for Afghanistan before delivering his speech, he said.

(Reporting by Jeff Mason and Ross Colvin, Editing by Patricia Wilson and Eric Beech)