WASHINGTON -- President Obama will address the nation next Tuesday night on his vision of the way forward in Afghanistan, a White House official told Fox News.

"It's my intention to finish the job," Obama said Tuesday in the East Room of the White House at at a joint news conference with Prime Minister Manmohan Singh. "I feel very confident when the American people hear a clear rationale for what we're doing there and how we'll achieve our goals, they'll be supportive."

Obama is expected to announce he's sending 34,000 additional troops, short of the 40,000 requested by his top commander there, Gen. Stanley McChrystal.

The news comes as Obama held a "rigorous final meeting" Monday with his Afghanistan war council and was expected to announce his revised strategy for the eight-year-old conflict just after his Thanksgiving break.

Obama said Tuesday he will make his announcement "shortly."

"I can tell you, as I said before, it's in our strategic interest, in our national security interest to make sure that Al Qaeda and its extremist allies cannot operate effectively in those areas," he said. "We're going to dismantle and degrade their capabilities and ultimately dismantle and destroy their networks. And Afghanistan's stability is important to that process." 

Military officials and others expect Obama to settle on a middle-ground option that would deploy an eventual 32,000 to 35,000 U.S. forces. That rough figure has stood as the most likely option since before Obama's last large war council meeting earlier this month, when he tasked military planners with rearranging the timing and makeup of some of the deployments.

Congressional hearings would follow the president's address, including testimony from McChrystal and U.S. Ambassador to Afghanistan Karl Eikenberry, whose concerns about support forces to help the Afghan military stand up on its won were seen as critical in delaying a final decision by the president.

Others who could take part in hearings would be Secretary of State Hillary Rodham Clinton, Defense Secretary Robert Gates. All four were among the approximately 20 top administration officials and Obama advisers participating in the talks Monday night -- one of the biggest groups gathered for these sessions in some time.

A senior military official said the hearing will likely be in the first or second week in December though a date has not yet been set. McChrystal is being prepared to arrive in the United States next week.

Rep. Howard "Buck" McKeon, the top Republican on the House Armed Services Committee, said Republicans are anxious to hear from McChyrstal and Eikenberry.

"General McChrystal's top priority is to stay focused on leading our armed forces to success in Afghanistan. However, it is essential that he and Ambassador Eikenberry be made available to testify before the Armed Services Committees," McKeon said in a statement. "Our troops, our allies, the Afghans and the entire international community are anxious to hear directly from the president and his battlefield commander on the way forward in Afghanistan."

The president has said with increasing frequency in recent days that a big piece of the rethinking of options that he ordered had to do with building an exit strategy into the announcement -- in other words, revising the options presented to him to clarify when U.S. troops would turn over responsibility to the Afghan government and under what conditions.

As White House press secretary Robert Gibbs put it to reporters on Monday, it's "not just how we get people there, but what's the strategy for getting them out."

Obama's two-hour Situation Room session Monday night was aimed at discussing "some of the questions that the president had, some additional answers to what he'd asked for," Gibbs said.

The spokesman said the president left the war council meeting without announcing a decision to the group, but added it would become public soon.

"After completing a rigorous final meeting, President Obama has the information he wants and needs to make his decision and he will announce that decision within days," Gibbs said late Monday.

The force infusion expected by the military would represent most but not all the troops requested by Obama's war commander, for a retailored war plan that blends elements of McChrystal's counterterror strategy with tactics more closely associated with the CIA's unacknowledged war to hunt down terrorists across the border in Pakistan.

McChrystal presented options ranging from about 10,000 to about 80,000 forces, and told Obama he preferred an addition of about 40,000 atop the record 68,000 in the country now, officials have said.

Obama has already ordered a significant expansion of 21,000 troops since taking office. The war has worsened on his watch, and public support has dropped as U.S. combat deaths have climbed.

The additional troops would be concentrated in the south and east of Afghanistan, the areas where the U.S. already has most of its forces, military officials said. The new troops that already went this year were directed to help relieve Marines stretched to the limit by far-flung postings in Helmand province and that would continue, while the U.S. effort would expand somewhat in Kandahar.

The increase would include at least three Army brigades and a single, larger Marine Corps contingent, officials said.

All officials spoke on condition of anonymity because the decision is not final.

Click here to read Fox News' interview with former U.S. ambassador to Afghanistan.

The Associated Press contributed to this report.