WASHINGTON — President Obama said on Tuesday that he will announce his decision on how many more troops to send to Afghanistan next week, and that it is his intention to “finish the job” that began with the overthrow of the Taliban government in the fall of 2001.

Mr. Obama, offering a tantalizing preview of what looms as one of the momentous decisions of his presidency, said he would tell the American people about “a comprehensive strategy” embracing civilian and diplomatic efforts as well as the continuing military campaign.

While he avoided any hints of the new troop levels he foresees in Afghanistan, the president signaled that he will not be talking about a short-term commitment but rather an effort muscular enough to “dismantle and degrade” the enemy and ensure that “Al Qaeda and its extremist allies cannot operate” in the region.

The president commented during an appearance with Prime Minister Manmohan Singh of India after what Mr. Obama called a “detailed discussion” of regional issues with the Indian leader, including Afghanistan.

Mr. Obama said he would talk about the “obligations” of America’s allies in fostering peace in Afghanistan, and that the United States would be acting not unilaterally but rather as part of “a broader international community.” And it will be up to the Afghan people to bring security to their homeland, with the help of training and other outside assistance, the president said.

The president spoke soon after administration officials said he had conducted the final meeting of his military review for Afghanistan, and that he is planning to explain his decision in an address to the nation, probably next Tuesday. Mr. Obama did not specify a day for his speech, and he jokingly told journalists he had already given them “a sufficient preview to last until after Thanksgiving.”

The chief White House spokesman, Robert Gibbs, said Tuesday morning that “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.”

For two hours on Monday evening, Mr. Obama held his ninth meeting in the Situation Room with his war council. The session began at 8:13 p.m., aides said, and ended at 10:10 p.m.

Mr. Obama’s military and national security advisers came back to him with answers he had requested in previous meetings, most of which focused on these questions: Where are the off-ramps for the military? And what is the exit strategy?

The conversation settled around sending about 30,000 more American troops, two officials said, the first of which would deploy early next year to be in place in southern or eastern Afghanistan by the spring. The troop reinforcements would most likely be sent in waves, according to an official speaking on condition of anonymity to discuss war strategy.

The White House has indicated recently that Mr. Obama has been studying several alternative approaches — including varying numbers of troops — with the intent of picking what he considers the best features of each.

Mr. Obama did not announce his specific decision to his advisers. He is scheduled to stay at the White House over the Thanksgiving holiday to finalize his decision, as the White House plans to prepare for what could be Mr. Obama’s first prime-time address to the nation from the Oval Office.

The venue of the announcement has not been decided, however. While an Oval Office address fits the gravity of the moment, one official said Tuesday that a full-length speech — rather than a short message, delivered as the president sits behind a desk — is a more likely way for Mr. Obama to explain one of the most important decisions yet in his presidency.

For the first time, Peter R. Orszag, director of the Office of Management and Budget, joined the group of advisers in the White House Situation Room on Monday evening — a strong indication that the president’s address would allude to the enormous costs of the military effort.

A photograph released by the White House shows Mr. Orszag sitting four seats from the president, next to Susan Rice, the United States ambassador to the United Nations.

As the White House prepares for how Mr. Obama will explain his decision to the nation, the president is trying to allay deep concerns within his own party.

The first in a series of meetings with Congressional leader will come later on Tuesday, when Mr. Obama plans to meet at 3:10 p.m. in the Oval Office with Speaker Nancy Pelosi. That meeting is to be followed by a private session with Mr. Obama, Vice President Joseph R. Biden Jr. and Defense Secretary Robert M. Gates at 4:30 p.m.

The White House is preparing for the president’s announcement to take place next Tuesday evening, aides said, which would probably be followed by hearings in the House and Senate. But the date could be changed, one official said, depending on briefings with Congress and allied leaders.

While Mr. Obama is expected by several of his advisers to announce sending more than 20,000 new troops — perhaps closer to the 40,000, as recommended by Gen. Stanley A. McChrystal — the White House is working to make the announcement more than about simply the number of troops. It will include an outline of an exit strategy, officials said.