President Obama’s national security adviser, Gen. James L. Jones, said on Sunday that a recommendation to send another 40,000 American troops to Afghanistan was just one part of a review of overall strategy that included such factors as a larger role for the Pakistani military and the integrity of the recent Afghan elections.

“It would be a mistake to underestimate the importance of other elements of the strategy,” General Jones said in an appearance on CBS’s “Face the Nation.” General Jones offered no endorsement of a recommendation by Gen. Stanley A. McChrystal, the top American commander in Afghanistan, to add another 40,000 troops on top of the 68,000 Americans already deployed there. At one point he described Gen. McChrystal’s recommendation as “his opinion” of “what he thinks his role within that strategy is.”

The comments by General Jones seemed to expose the debate within the Obama administration on committing more troops. On Saturday, eight Americans and two Afghan policemen were killed in a daylight attack against two American outposts.

In an appearance on CNN’s “State of the Union,” General Jones asserted that he does not believe Afghanistan is “imminent danger of falling” to the Taliban and that the presence of al Qaeda “is very diminished.”