The session followed a meeting Tuesday with congressional leaders that at times was contentious, including a pointed exchange with Sen. John McCain over the pace of deliberations.
The top U.S. commander in Afghanistan, Gen. Stanley McChrystal, is seeking up to 40,000 additional troops but some of the president's war advisers along with some key Democrats are wary of escalating the war.
Among those expected to attend Wednesday's meeting are Vice President Biden, Secretary of State Hillary Clinton, Gates and McChrystal via videoconference.
Wednesday's meeting came on the eighth anniversary of the beginning of the war in Afghanistan.The Senate Foreign Relations Committee was holding a hearing seeking more information on Al Qaeda and the threat it poses in Afghanistan.
Obama, who inherited the war when he took office last January, is examining how to proceed with a worsening combat situation that has claimed nearly 800 U.S. lives and sapped American patience. Launched after the Sept. 11, 2001, terrorist attacks to defeat the Taliban and rid Al Qaeda of a home base, the war has lasted longer than ever envisioned.
"The bottom line is the clock is ticking," retired Gen. Bob Scales told FOX News. "And it's all driven not by politics but it's driven by conditions on the ground."
"One has to get a strategy that works, a strategy that has confidence of everyone involved, then get the resources," he said. "The president is determined not to do this backwards. ... Once and for all after eight years, we're going to get this right."
But Republicans support McChrystal's troop request and are critical of Obama's deliberations.
"We are witnessing a profound lack of focus," House Republican Conference Chairman Mike Pence, R-Ind., said Wednesday.
House Minority Whip Eric Cantor, R-Va., said Republicans are ready to support the president if he makes the right decision.
House Minority Leader John Boehner added that the president has a difficult decision in front of him.
"I'm hopeful the president comes to a decision soon," he said. "No one wants him to make this decision in haste."
House and Senate leaders of both parties emerged Tuesday from a nearly 90-minute conversation with Obama with praise for his candor and interest in listening. But politically speaking, all sides appeared to exit where they entered, with Republicans pushing Obama to follow his military commanders and Democrats saying he should not be rushed.
Obama said the war would not be reduced to a narrowly defined counterterrorism effort, with the withdrawal of many U.S. forces and an emphasis on special operations forces that target terrorists in the dangerous border region of Afghanistan and Pakistan. Two senior administration officials say such a scenario has been inaccurately characterized and linked to Vice President Joe Biden, and that Obama wanted to make clear he is considering no such plan.
The president did not show his hand on troop increases. His top commander in Afghanistan, Gen. Stanley McChrystal, has bluntly warned that more troops are needed to right the war, perhaps up to 40,000 more. Obama has already added 21,000 troops this year, raising the total to 68,000.
Obama also gave no timetable for a decision, which prompted at least one pointed exchange.
Inside the State Dining Room, where the meeting was held, Obama's Republican opponent in last year's presidential race, Sen. John McCain, told Obama that he should not move at a "leisurely pace," according to people in the room.
That comment later drew a sharp response from Obama, they said. Obama said no one felt more urgency than he did about the war, and there would not be nothing leisurely about it.
Obama may be considering a more modest building of troops -- closer to 10,000 than 40,000 -- according to Republican and Democratic congressional aides. But White House aides said no such decision has been made.
The president insisted that he will make a decision on troops after settling on the strategy ahead. He told lawmakers he will be deliberate yet show urgency.
"We do recognize that he has a tough decision, and he wants ample time to make a good decision," said House Republican leader John Boehner. "Frankly, I support that, but we need to remember that every day that goes by, the troops that we do have there are in greater danger."
What's clear is that the mission in Afghanistan is not changing. Obama said his focus is to keep Al Qaeda terrorists from having a base from which to launch attacks on the U.S or its allies. He heard from 18 lawmakers and said he would keep seeking such input even knowing his final decision would not please them all.
Obama's emphasis on building a strong strategy did not mean he shed much light on what it would be. He did, though, seek to "dispense with the more extreme options on either side of the debate," as one administration official put it. The official spoke on condition of anonymity to discuss details of the closed-door meeting.
The president made clear he would not "double down" in Afghanistan and build up U.S forces into the hundreds of thousands, just as he ruled out withdrawing forces and focusing on a narrow counterterrorism strategy.
"Half-measures is what I worry about," McCain, R-Ariz., told reporters. He said Obama should follow recommendations from those in uniform and dispatch thousands of more troops to the country -- similar to what President George W. Bush did during the 2008 troop "surge" in Iraq.
Public support for the war in Afghanistan is dropping. It stands at 40 percent, down from 44 percent in July, according to a new Associated Press-GfK poll. A total of 69 percent of self-described Republicans in the poll favor sending more troops, while 57 percent of self-described Democrats oppose it.
The White House said Obama won't base his decisions on the mood on Capitol Hill or eroding public support for the war.
"The president is going to make a decision -- popular or unpopular -- based on what he thinks is in the best interests of the country," press secretary Robert Gibbs told reporters.
FOX News' Chad Pergram and The Associated Press contributed to this report.