The plan has not yet been approved, but military and political leaders say a renewed sense of urgency has taken hold, as the deadline approaches for the Obama administration to begin withdrawing its forces from Afghanistan. Even with the risks, military commanders say that using American Special Operations troops could bring an intelligence windfall, if militants were captured, brought back across the border into Afghanistan and interrogated.

The Americans are known to have made no more than a handful of forays across the border into Pakistan, in operations that have infuriated Pakistani officials. Now, American military officers appear confident that a shift in policy could allow for more routine incursions…

The decision to expand American military activity in Pakistan, which would almost certainly have to be approved by President Obama himself, would amount to the opening of a new front in the nine-year-old war, which has grown increasingly unpopular among Americans. It would run the risk of angering a Pakistani government that has been an uneasy ally in the war in Afghanistan, particularly if it leads to civilian casualties or highly public confrontations.

Still, one senior American officer said, “We’ve never been as close as we are now to getting the go-ahead to go across.”